Audio Super-Resolution with Latent Bridge Models
Authors: Chang Li
Zehua Chen
Liyuan Wang
Jun Zhu
Venue: NeurIPS 2025 poster ()
Keywords: audio super-resolution
latent bridge models
cascaded models
audio generation
audio enhancement
Primary area: deep_learning

Abstract: Audio super-resolution (SR), i.e., upsampling the low-resolution (LR) waveform to the high-resolution (HR) version, has recently been explored with diffusion and bridge models, while previous methods often suffer from sub-optimal upsampling quality due to their uninformative generation prior. Towards high-quality audio super-resolution, we present a new system with latent bridge models (LBMs), where we compress the audio waveform into a continuous latent space and design an LBM to enable a latent-to-latent generation process that naturally matches the LR-to-HR upsampling process, thereby fully exploiting the instructive prior information contained in the LR waveform. To further enhance the training results despite the limited availability of HR samples, we introduce frequency-aware LBMs, where the prior and target frequency are taken as model input, enabling LBMs to explicitly learn an any-to-any upsampling process at the training stage. Furthermore, we design cascaded LBMs and present two prior augmentation strategies, where we make the first attempt to unlock the audio upsampling beyond 48 kHz and empower a seamless cascaded SR process, providing higher flexibility for audio post-production. Comprehensive experimental results evaluated on the VCTK, ESC-50, Song-Describer benchmark datasets and two internal testsets demonstrate that we achieve state-of-the-art objective and perceptual quality for any-to-48 kHz SR across speech, audio, and music signals, as well as setting the first record for any-to-192kHz audio SR. Demo at https://AudioLBM.github.io/.

Audio Super-Resolution with Latent Bridge Models
Chang Li 12,,. Zehua Chen 1.2, Liyuan Wang' Jun Zhu 122
Department of CST, Tsinghua University, Beijing, China Shengshu AI, Beijing, China USTC, Hefei, China
(zhc23thuml, liyuanwang, dcszj) @tingguu edu, 1c lc_lca@mail. ustc. edu. cn
Abstract
Audio super-resolution (SR), i.e., upsampling the low-resolution (LR) waveform to the high-resolution (HR) version, has recently been explored with diffusion and bridge models, while previous methods often suffer from sub-optimal upsampling quality due to their uninformative generation prior. Towards high-quality audio super-resolution, we present a new system with latent bridge models (LBMs), where compress the audio waveform into continuous latent space and design LBM to enable a latent-to-latert generation process that naturally matches the I--tt-- HR upsampling process, thereby fully exploiting the instructive prior information contained in the LR waveform. To further enhance the training results despite the limited availability of HR samples, introduce frequency-awe -wware LBMs, where the prior and target frequency are taken as model input, enabling LBMs to explicitly learn an any-to-amy upsampling process at the training stage. Furthermore, we design cascaded LBMs and present two prior augmentation strategies, where we make the first attempt unlock the audio upsampling beyond 48 kHz and empower seamless cascaded SR process, providing higher flexibility for audio post-production. Comprehensive experimental results evaluated on the VCTK, ESC-50, Song- Describer benchmark datasets and two internal testsets demonstrate that we achieve state-of-the-arr objective and perceptual quality for any-to-48kHZ SR across speech, audio, and music signals, as well setting the first record for any-to-192kHz audio SR. Demo at http://AudioLLBMMgihhhh
1 Introduction
Audio super-resolution (SR) systems aim to generate the high-resolution (HR) audio waveform
from the observed low-resolution (LR) waveform 47 56 [09]. Audio SR plays crucial roles
in various applications, including historical recording restoration 773 59 74], hearing aids [30],
and improvement perceptual quality [62]. Previous works have explored audio with diverse methods such as mapping-based (60, (9). generative adversarial network (GAN)-based [69 65).
diffusion-based [72] 62]. and recently proposed bridge-based [54] 45) methods. However, these efforts focus the audio SR task in limited scope, e.g., the speech signals in benchmark dataset, without generalizing to a broader domain of different audio types. To extend audio SR to multiple domains spanning speech signals, sound effects, and music samples, Liu et al. [62] has recently explored diffusion models in the latent space of mel-spectrogram, enabling any-to-48 kHz audio SR. A SB [5] has recently explored bridge models to synthesize the short-time Fourier transformation (STFT) representation, achieving any-to-44. kHz music SR.
"quual Contribution.
Corresponding Authors: Zehua Chen and Jun Zhu.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

However, the quality of audio SR at scale is still lim- ited. One major cause is the potential mismatch be- tween their generative frameworks and the audio SR process. As shown Fig. 2 AudioSR [62] synthe- sizes the missing part of the mel-spectrogram latent representation from an uninformative Gaussian prior,
4.5
Generation Results
AudioSR
Meen Opinion Soore
Audiol BM (Ours)
3.5-
ignoring the fact that the LR waveform contains infor-
3.0
mative cues about the HR target. SB (45] formu- lates the audio SR analogous to image inpainting [58]. where the removed regions are filled with Gaussian priors that remain uninformative about the target sig- nal. Aiming for a high-quality audio SR system, we propose latent bridge model (LBM) named Audi- oLBM, learning the L.R-to-HR waveform SR process with datent-to-latent generative framework. Specif- ically, we directly compress the audio waveform into continuous latent representation, where the latent of the LR waveform demonstrates instructive infor- mation for the latent of the HR waveform and avoids the removed areas in previous works Then, we design bridge models [14] [30 to enable a latent-to toeete-to-latet generation process, which is inherently matched with the LR-to-HI HH waveform SR task and fully exploits the informative prior in the latent space.
2.0
MaskGCT
Audiol DM2 16 KHZ
QA-MDT 16 kHz
24 WHZ
Figure 1: Audio significantly improves the perceptual quality of ext-to--ppeec [ text-to-audio [63], and text-to-music [53] gen- eration, and outperforms the sfate-of-the-art any-to-48 kHz SR system AudioSR 62
Given the scarcity of high-resolution audio samples, which limits the generalization and scalability of audio SR systems, we propose frequency-aware LBMs that incorporate the prior and target frequencies as explicit conditioning imputs. The awareness of the frequency both boundary distributions enables AudioLBMr to explicitly learn an any-to-any upsampling process across different frequency bands the training stage, leading improved upsampling performance the target resolution the sampling stage. Furthermore, upsampling the audio signal to a higher sampling rate, such as 96 or 192 kHz. provides enhanced high-frequency detail and allows flexibility audio post-production. regard, we demonstrate that AudioLBM can be naturally extended to unlock the audio upsampling beyond 48 kHz with a cascaded design, where we present the prior augmentation strategies to reduce the cascading error in inference and the fine-tuning techniques to facilitate 192 kHz upsampling.
this
In summary, we make the following contributions in this work:
We present high-quality audio SR system across speech, sound effects, and music samples through modeling the LR-to-HR process with latent-to-latent generative framework.
We propose frequency-awars LBMs and cascaded LBMs, enabling an any-to-any training process to overcome data scarcity and empowering SR beyond 48 kHz for the first time.
Zero-shot any-to-48 kHz audio SR evaluated on VCTK [188, Song- Describer- Dataset (68), and ESC-50 799 demonstrate that our method outperforms prior systems with an average improvement of 21.5% in LSD 255 and 3.05% in ViSQOL [15] across audio and music, as well as achieves state-of-the-art objective and perceptual quality [7 for speech upsampling.
2
Related Work
Audio super-resolution. and waveform-based methods. Spectral-based methods, often referred to as bandwidth extension (BWE). formulate the task as a spectral inpainting problem in either time-frequency space [60]
Previous works audio SR can be broadly categorized into spectral- -base
[59 69 96. 72 [12,, 126] 19 46) or latent spectral space [62] 37 In contrast, waveform-
based methods directly generate high-resolution signals the time domain 47
76
49
32
125 51
54 However, most existing works remain limited in specific domains such as speech or isolated
music genres [73 [7I] and are evaluated under fixed input resolutions 669 65
96), simplified
69 These limitations hinder generalization to real-world scenarios involving diverse content and degradation types, such as polyphonic pop music that combines vocals, background instrumentation, and sound effects, or handling extremely low-resolution inputs. Moreover, performing SR beyond 48 kHz (e.g., 96 kHz and 192 kHz) remains unexplored, which provides further benefits in various professional applications,
degradation assumptions [32 55), or limited output sampling rates [72 46

---

LR Waveform
Audio, Speech and Music Super-Resolution
HR Waveform
Chebyshev Filters
MM M
Butter Filters
Elliptic Filters
XER
E
STFT MelFB
N
Vocoder
Eone
Ererr
E
TT
Zx E R
2x E R
'
Eeno
Edec
Zz RR CC
2g R xC
Figure 2: The top part shows how the low-resolution waveform is simulated during training via low-pass filtering, the middle part depicts the baseline method AudioSR [62] that synthesizes high- resolution content from Gaussian noise, and the bottom part presents overview of proposed AudioLBM. learns a latent-to-later generation process between the low- and high-resolution
waveform latent representations, namely = E length. Cg and Te are the channel dimension and compression ratio of waveform latent. contrast, AudioSR operates in latent space x E IR x xx of mel-spectrogram X E FxT with noise- to-latent generation process, where T and F denote time and frequency bins of mel-spectrogram; ex and rxx denote channel dimension and compression ratio of mel-spectrogram latent.
x To and = E R "r, where L is waveform
including mastering [57 post-production 77, spatial audio 8 and immersive content creation 101 Although AudioSR 62 stands out as scalable method achieving any-to-48 kHz SR across diverse domains, it suffers from two-stage compression pipeline and sub-optimal generative modeling paradigms for the SR task, leading to sub-optimal low-frequency fidelity, misalignment across frequency bands, and high-frequency artifacts [[31], which ultimately limit perceptual SR quality. Therefore, building unified and high-fidelity audio SR model that scales across speech signals, sound effects, and music samples remains a critical challenge. Detailed discussion of audio SR baseline methods is provided in Appendix H.2.2
Bridge models. Tractable bridge models 130 64 52 have received increasing attention for
enabling more effective and efficient data-to-data generation paradigms. Unlike diffusion models [34 988 that generate data by reversing Markov process that gradually injects noise into the input, bridge models begin from deterministic and informative prior, and interpolate stochastically toward the target distribution. Recent studies have explored bridge models in various applications, including image translation
[52 103,, image restoration (88 18), dense prediction [38], image editing [I],
quality assessment [128 129 and text-to-speech synthesis [14). Building this paradigm, Bridge- SR [54) applies the Schrödinger Bridge (SB) framework directly the waveform domain for speech SR. using lightweight WaveNet-based score estimator [106] 44]. In parallel, ABBB (45) employs the SB formulation the STFT domain for music bandwidth extension and inpainting using a U-Net backbone 88 22]. However, directly modeling in the data space inherently limits generalization and poses challenges for stable training and flexible scaling to higher- resolution SR. These limitations motivate to develop more adaptive generation framework tailored audio SR.
Method
In this section, we introduce a latent bridge model (LBM) named AudioLBM to achieve high-quality super-resolution (SR). The key innovations include bridge-based audio upsampling in the continuous latent space of waveform, the frequency-aware model training process, and the cascaded design that unlocks audio SR beyond 48 kHz.

---

3.1 AudioLBM
Considering that the observed LR waveform has been an informative prior of the target HR waveform in the time-domain [54], we train a convolution-basee compress the audio waveform into continuous representations, preserving the prior contained in the LR waveform for target generation. The details of VAE architecture and training configurations are introduced in Appendix[B, Given the HR audio waveform z. E RR,, we compute the LR counterpart aLR E IR_ with various low-pass filters to simulate the real-world degradations. Then, we compress them into latent representations ZHR E Rext and 2LR Rext with a pre-trained encoder (x)), where I and rs the down- nown-sampling factor, constructing the boundary distributions and establishing the bridge process as follows.
variational autoencoder (VAE) [26] to directly
Bridge process. Given LL E Rext as the prior 2y at time step t = and HR E Rox! as the target 2u time step = O, build bridge process [4] to connect the boundary distributions (see details in Appendix Ch:
0.5 of
O. of
2T 0,00O; 6, 6 6~ I),,
Zo +
where 2, denotes the noisy representation at time step in the forward process of bridge models, and ag,, 0,2g dz, define the drift and diffusion terms in the associated stochastic differential equation (SDE), thereby controlling the noise schedule of the bridge process. Different from the forward process of diffusion models transforming the clean representation the beginning f into standard Gaussian noise at the boundary t T, bridge models replace the uninformative Gaussian prior with Dirae prior بuLx, and therefore facilitate the generation process fully exploit the instructive information contained in the prior distribution i.e., 2R LR in AudioLBM.
Training objective. There exist multiple equivalent training objectives for bridge models. We empirically find that the latent space, our AudioL.BM achieves higher synthesis quality by using a noise predictor, compared to the data predictor used by recent bridge-related works in waveform [54] or specstrctroormm domain [1]]. this regard, we formulate the denoising objective as:
27
2t 0g
Liridge (0)
Eez== = by =x (.27
6/ 6o(2), 2T)
04
where z, is calculated with Eq. [I at each training iteration.
Sampling process. The forward process bridge models has reverse process sharing the same marginal distribution Pt (z(2/z0, (0, zr) [30] For signal generation, starting from the prior LR use first-order SDE-based sampler. From the time step s to the time step t [0, s), the first-order discretization gives:
i
2s + at (1- of Eo Eo(Zx, 8) + oorr
2,
C~N(O,T).
a,
Given noise predictor en well-trained with Eq. (2), we estimate the target 2n in Eq. 3 with 20 Zi
ozeg at each sampling step, and iteratively synthesize the generation target = The pre-trained decoder HR) of VAE is then used to reconstruct the waveform HR
Bridge process diffusion process. As shown in Fig. 2 the diffusion-basee audio upsampling employs a conditional noise-to-latent sampling trajectory, where the prior provides limited infor- mation for the target. In comparison, from ZL to 2 HR which has been aligned with the LRR-o-HH audio upsampling. Moreover, in the continuous latent space directly compressed from the audio waveform, the representation of LR waveform provides instructive information for the generation target, rather than suffering from area removal in latent space compressed by the STFT representation
method employs latent-to-latent sampling trajectory
451
mel-spectrogram [22
3.2 Frequency-awann aware LBMs
Compared to most text-to-speech 111
or text-to-audio 61 63
27
50
generation systems that
synthesize the audio samples at sampling rate below 24 or 44.1 kHz, it is more expensive to collect

---

the audio samples at sampling rate of 48 kHz for training audio sampaing models. To address the limitation of dataset scale, we propose frequency-aware LBMs, enabling an any-to-any upsampling process at the training stage. Specifically, given an audio signal a E RR,, we first filter an HR waveform HH TR_ with a sampling rate SRanSthar is lower than the sampling rate of æ. while has already provided the frequency band where the audio information predominantly concentrates (detailed in Appendix C). Then, we compute the LR version æL E g² with a sampling rate SR uniformly sampled from UZ (0, SR constructing new LR-HR data pair rather than using fixed sampling rate for HH
At each training iteration, we first compress the मh and x into latent 2 HR and x 2 and then take their sampling rate ,R and SR as model input, encouraging LBMs to explicitly learn an any-to-any upsampling process. Specifically, we extract sinusoidal embedding of quantized furzer Quantize /2) and continuous Sprior = SR /2 and prepend them as two additional tokens of our DiT 78 -based noise prediction network, expanding the feature space to Rex (1+2), Towards stronger training performance, we leverage the constant scaling factor for training bridge models in the waveform domain [54], rescaling the latent with & = $ * z for stable training, leading to the training objective of our frequency-awee awaree LBMs:
2. at &0
L CAudioLB((0) = Eio gHR Ey 24,
co t, žr, Spriors Stages)
(4)
where the noisy latent &, is computed from rescaled En and शn with Eq. T]. At inference, the detected prior frequency fprue and the target frequency Sunget = 48 kHz/2 = 24 kHz are both used to condition the model. Specifically, the input waveform low-pass pit-passsitteddd by Sprior to suppress fighffrequency artifacts, while furget guides the model to generate full-band output up to the desired resolution.
3.3 Audio SR beyond 48 kHz
Cascaded LBMs. Beyond 48 kHz, the audio at an ultra-high sampling rate (e.g., 96 kHz or 192 kHz) provides engineering advantages and post-processing flexibility [85]. However, scaling the upsampling system to such a sampling rate is constrained by the limited capacity of a single model and the scarcity of high-resolution training data, which has not been addressed to date. Here, we propose an extended version of AudioLBM that progressively improves the reconstructed signals from 48 kHz to higher sam- pling rates. Taking the upsampling to 96 kHz as an example, we introduce cascaded LBMs We first train VAE-based compression network UHR for the ultra HR audio waveform x UHR enabling us to design new AudioLBM c, !!HR in the latent space = _ At generation stage, the waveform L.. is first upsampled to IIl with the first-stage LBM, and then taken the input of the second-stage model, further upsampled to x: UHR with a latent-to-latent process from 2 HR to 2 UHR with Eq. (3), shown in Figure 3
LBM3
Aug
LBM2
LBM1
Aug
16 kHz
48 kHz
96 kHz
192 KHz
Figure 3: LBMs can be naturally extended into higher-resolution waveform generation with a cascaded paradigm, where prior aug- mentation is utilized to avoid cascading arti- facts and accumulating errors between stages.
In the scenario of 192 kHz upsampling, third-stage LBM is cascaded. However, as the data has been extremely expensive to collect, which restricts the model performance, we propose fine-tuning method leverage the pretrained LBM at the second stage, improving the synthesis quality.
Prior augmentation. One of the potential limitations of cascaded generative models is the cascading errors in inference [35]. In cascaded LBMs, the LBM at the first stage approximates the ground- truth distribution of x HR while we inevitably suffer from a mismatch between the synthesized data and the GT signal because of the imperfect learning of eg. Hence, we propose two prior
'To avoid ambiguity, we define the low-pass filter (LPF) by its sampling rate, corresponding to filtering with cutoff at its Nyquist frequency.
5

---

augmentation strategies in the waveform and latent space. respectively. for the cascaded bridge models & alleviating the mismatch issue with the first-stage LBM Eg and therefore strengthening the upsampling performance. Firstly, considering the difficulty for generative models to reconstruct fine-grained waveform features, we introduce degradation operation the waveform domain. Specifically, in the second upsampling stage, we randomly remove small portion of high-frequency details near the Nyquist boundary of the prior and obtain a pww-pas-filtered waveform, denoted as LPF(x Furthermore, solely simulating the previous stage's s output via waveform degradation is insufficient to address potential large-scale artifacts, which may be reflected unclear harmonics or imbalanced energy distribution. To mitigate this, further introduce latent-space blurring, which perturbs the audio by applying dynamic Gaussian smoothing to its latent representation along the time axis. Unlike previous diffusion-basse based [35] or flow-based [95] methods where the latent is corrupted with random noise for augmentation, the blurring strategy provides a deterministic degradation that aligns with the Dirae boundary distributions in bridge models [14], leading the following training objective for the cascaded bridge model co
UHR,
2, 20
fy= (0) Bur (0=l(00)
UHR E6 (Zt: 1, 2HR Sprrios Starget; br)
(5)
where E, is calculated with the the ground-truth target UUHR and the blurred latent prior Blur( ( the condition zHR is the rescaled latent compressed from the degraded waveform LPF((HHRR: ); the condition b, ((, brin) is the blurring ratio. Hence, the degradation level also conditioned into the LBM with fprir and by. In the training of cascaded LBMs Eg
UIR the small-scale details
of the ground-truth prior HR has been removed and then the latent prior is blurred, enforcing the model model the generation of z _UHR from a degraded prior Blur(=Hk) and therefore facilitating the cascaded upsampling process in robust manner. Further training details of cascaded are provided in Appendix D At inference time, we select the optimal parameters 67 and waveform filtering extent via grid search to maximize cascading quality.
4
Experiment
In this section, we first describe the experimental setups and then present the experimental results of any-to-48 kHz upsampling and upsampling beyond 48 kHz with an in-depth analysis.
4.1 Experimental setup
Training setup. We train our compression and SR models on a mixed corpus comprising speech, audio, and music data. All recordings with an original sampling rate below 32 kHz are filtered out, resulting in a total of approximately 5,000 hours of training data. The detailed dataset information is summarized in Appendix G For each SR stage, all data are resampled to the corresponding target sampling rate and randomly cropped for 5. 12-seond for the any-1o-48 k/fz and 48 48-99 kHz models and 2.56-second segments for the 96 196 kHz upsampling stage.
We apply dynamic low-pass filtering to simulate real-world complexity. For the any-to-48 kHz stage, the cutoff frequency is sampled from (1,000,, 20,000) Hz, the filter type is randomly chosen from (Chebyshev, Butterworth, Bessel, Elliptic). and the order is sampled from (2, 10). For the 48-96 kHz and 96->199 kHz stages, we exclusively use a Chebyshev Type-I filter with order 8 and sample cutoff frequencies from (16,0000, 48,00 48,000) Hz and (32 (3,,000, 96,000), respectively. This design supports arbitrary input sampling rates in any stage and naturally serves as deterministic waveform-basee degradation strategy, as described in Sec. (.3 For cascading inference, we filter off
a frequency range of 4 kHz as waveform degradation and j 1.0, b, 0.3 for latent degradation for both 96 kHz and 192 kHz SR.
Evaluation setup. For the any-to-48 kHz task, we randomly sample 500 speech clips from the VCTK [18 test set, 300 audio samples from the ESC-50 fold-5 (79 and 300 music samples from the Song- Desteeeerbbbrr-tttteet (SDS) 68 Since both ESC-50 and Song-Describer are natively recorded at 44.1 kHz, we resample all model outputs to 44.1 1 kHz to ensure fair comparison. To evaluate performance on native 48 kHz content, we additionally use 300 randomly selected clips from our internal 48 kHz dataset (48Audio). For the 96 kHz and 192 kHz settings, select 300 audio clips

---

VCTK
kHz +48 kHz
Metric
Input
UDM+
NW1
NW2
NVSR
Frep
FlowH
APBE
BriSR*
AuSR
Ours
Ourst
LSD1
4,069
1.232
1.417
1.141
1.003
0.907
0.816
1.003
1.047
0.940
0.753
0.742
LSD(LN
0.187
0.216
0.268
0.294
0.357
0.272
0.194
0.224
0.172
0.486
0.773
0.708
LSD(I)
4,456
1.345
1.544
1,239
1.085
0.985
0.889
1.093
1.143
0.994
0.724
0.712
SSIM
0.519
0.691
0.661
0.654
0.734
0.755
0.784
0.742
0.660
0.809
0.893
0.906
SigMOSt
3.136
3.068
2.936
2.838
2.831
2.743
2.792
3.082
2.998
2.846
3.023
3.095
Metric
Input
AuSR
Ours
Input
AuSR
Ours
Input
AuSR
Ours
Input
AuSR
Ours
48Audio
8 kHz +48 kHz
12 448 kHz
16 kHz +48 kHz
24 kHz +48 kHz
L.DD
2.931
1.468
1.066
2.637
1.365
0.981
2.351
1.304
0.893
1.788
1.234
0.845
ViSQOLt
2.714
3.156
3.281
2.905
3.242
3.331
3.055
3.303
3.509
3.454
3.622
3.801
ESC-50
8 kHz
+44.1
kHz
12 kHz
+44.1 kHz
16 kHz
+44.1
kHz
24 kHz
+44.1 kHz
LSD4
3,042
1.537
1.190
2.720
1.412
1.087
2.435
1.292
0.999
1.810
1.067
0.947
ViSQOLt
2.604
2.961
3.003
2.642
3.031
3.089
2.777
3.108
3.234
3.609
3.602
3.641
SDS
kHz
+44.1
kHz
12 kHz
+44.1
kHz
kHz
+44.1
kHz
24 kHz +44.1 kHz
LSD1
4.515
1.728
1.338
4.070
1.501
1.223
3.632
1.352
1.160
1.788
1.166
1.110
ViSQOL
1.712
2.714
2.744
1.833
2.905
2.939
2.155
3.055
3.168
3.377
3.454
3.603
Table Objective and perceptual metries across speech, audio, and music. Baselines marked with * are our re-implementationn. Ourst denotes our model trained exclusively on the VCTK training set.
(96/192 Audio) and 300 music (96/192 Music) excerpts from our internal dataset. Each 192 kHz clip is 2.56 seconds long, while all other evaluation samples are 5.12 seconds.
Long duration inference can be readily implemented using the MultiDiffusion
5
20 39 framework,
and we empirically find that employing larger overlap sizes in the early sampling steps, while using smaller ones but shifting window positions in the later steps (even 0), is more effective in improving consistency and quality with LBMs.
For objective evaluation, we report the widely used Llg-Speecrall Distance (LSD) 25 and Spectral Structural Similarity (SSIM) [113, (59). To assess perceptual quality, we use ViSQOL 15 for 48 kHz
general audio and music, and SigMOS 87 for 48 kHz speech.
Baseline method. For evaluation under the any-to-48 k/lz setting, unless specifically noted, we report only our zero-shot results without post-processing// 62 60) for low-frequency replacement. For speech, in addition to AudioSR (AuSR) (62). we compare against speech-specifts baselines trained
on the VCTK -tain set, including UDM+ [20), NU-Wave (NWI) [4),, NU-Wave2 (NW2) (32).
NVSR [60] FlowHigh (FlowH) 122 Frepainter (Frep) 41. AP-BWE (65). and Bridge-SR (BriSR*) ) parameters, and retrain it on both the VCTK set and our training dataset. For general audio and music, we compare with AudioSR under the any-to-48 kHz configuration. As there are no publicly available baselines for the 96 kHz and 192 kHz settings, we conduct only ablation studies using our own models. We scale our any-to-48 kflz model to 0.5B parameters, while the two subsequent models are scaled to 0.3B. All models are trained with an effective batch size of 128 and IM iterations, while the fine-tuming line-tuning procedure described in Sec. 3.3 takes an additional 0.5M steps. Unless otherwise specified, all ablation experiments are conducted with the same model size, using effective batch size of 32 and trained for 0.2M steps without speech data. We use First-Order SDE sampling [4]] for 50 steps for all stages. The compression architecture and additional model details are further discussed in Appendix
54 We follow the original Bridge-SR configuration, scale up the network to 10.6M
4.2 Any-to-48 kHz upsampling
Overall performance. As shown in Table 1 we evaluate our method across speech (48 kHz), gen- eral audio (48/44.1 kHz), and music datasets (44.1 1 kHz) using both objective metries and perceptual scores. For the 8 kHz->48 kHz speech SR task, probabilistic generative approaches 62 122 as
7

---

Dataset
ESC-50 (Audio, 16 kHz +48 kHz)
SDS (Music, 16 kHz +48 kHz)
w/o Filter
w/o Input-A
w/o Target-A
Ours
only
w/o Filter
w/o Input-A
w/o Target-A
Ours
only
Metric
48 kHz
48 kHz
LSD4
1.366
1,052
1.022
0.994
1.127
1.461
1.187
1.166
1.124
1.198
LSD-HF
1.448
1.093
1.069
1.026
1.173
1.567
1.262
1.239
1.192
1.275
SSIM
0.701
0.715
0.721
0.722
0.711
0.466
0.477
0.478
0.484
0.478
Table 2: Ablation studies on ESC-50 and SDS for the 16 kHz->48 kHz SR setting. Input-A denotes uppu-frrquency awareness; Target-A denotes farget-fr awareness.
16 996 kHz on 96Audio and 96Music
16->192 kHz on 192Audio and 192Music
Metric
Input
Direct
Ours
Metric
Input
Direct
48 kHz
96 kHz
Ours
LSD1
3.068
1.406
1.216
LSD4
2.929
1.913
2.744
2.314
1.365
LSD (0-48)4
4.006
1.498
1.083
LSD -64
3.191
1.452
2.304
1.372
1.160
ViSQOLt 2.562
3.010
3.330
LSD (96-
2.880
2.244
2.879
2.879
1.474
Table Comparison of super-resolution performance on 96 kHz and 192 kHz targets. Direct refers to directly trained any-to-96/193 kHz models. The 48 kHz and 96 kHz columns indicate intermediate outputs in the cascaded pipeline.
well as our method demonstrate clear advantages in capturing global spectral structure (SSIM) and high-frequency quality (LSD(H)). Notably, our zero-shot model significantly outperforms all previous methods in objective evaluation, reducing LSD-HF from FlowHigh's 's 0.889 to 0.724, improving SSIM from AudioSR's 0.809 0.893, and achieving higher perceptual quality (3.023 vs. 2.846 in SigMOS). Due to the domain diversity of the zero-shot training set, we find that the low-frequenc, noise of speech some cases is amplified and mistaken for texture in sound effects, which can slightly degrade the perceptual quality. As a point of comparison, we further evaluate a variant trained only on VCTK-train (Ourst), which obtains even better performance and surpasses the GAN-based perceptual SoTA (65) (3.095 vs. 3.082 in SigMOS).
54 often preserve low-frequency components almost perfectly, as indicated by LSD(L) scores close to the input. However, they often struggle to generate high-quality high-frequency contents. Alternatively, other methods [12 60] [1 62] employ post-processing strategies that directly replace the low-frequency band with the original input, thereby achieving near-perfect preservation. In our case, since the model already demonstrates strong overall LSD performance, we refrain from using such replacement strategies (detailed in Appendix
It worth noting that the methods without compression networks [20 49
Ablation studies. We compare our AudioLBMs without filtering any low sampling-rate data (w/o Filter), without any frequency-awarenee (w/o Input A), sorely with input-awareness (w/o Target A) and with both input and target frequency awareness (Ours). As shown in Table the use of simple dataset filtering, input-fire freuuuffyueeccy awareness, and output- trepuu-freuencyy awareness leads to a steady and progressive improvement in 48 kHz SR performance. This leads to approximately a 20% reduction in LSD and a noticeable increase in SSIM across both audio and music domains, demonstrating the proposed frequency-awaree awareness mechanism under a moderately filtered dataset. Furthermore, the training solely on 48 kHz data significantly reduces the diversity and scale of the training set, leading to sub-optimal performance and notable drop in both LSD and SSIM. These results further validate the superiority of the proposed any-to-any training paradigm.
4.3 Upsampling beyond 48 kHz
Overall performance. Table 3 presents the comparison results under the 96 kHz and 192 kHz SR settings, where the input waveform is sampled at 16 kHz. We evaluate both cascaded LBMs and directly trained any-to-96/18 96/192 kHz LBMs. It can be seen that the cascaded LBMs consistently outperform the directly trained counterparts for SR beyond 48kHz. Benefiting from specific trained
8

---

Inpus
Nu. Wave
AudioSR
Frepainter
Flowlligh
Ours
Ground Truth
Inpur (16 KHb)
Ground Truth (48 kHz)
Figure 5: For case studies, we present the linear-amplitude STFT spectrograms of 1.5-second speech segment from the VCTK-test set (sample p360_1002 (02) and 5cco-o music clip.
models with sufficient quantity of corresponding audio data, the cascaded 96kHz LBMs achieves better content generation below 48kHz, reflected in 0.415 reduction in LSD (0-48) and a 0.32 improvement ViSQOL, which demonstrates the necessity of the cascaded paradigm. Furthermore, 0.212 reduction in LSD(16-96) under the 192 kHz setting indicates that the proposed prior and conditioning augmentation strategy effectively enhances and refines the content generated by the previous stage.
To validate the effectiveness of the frequency-aware training paradigm in higher-resolution SR scenar- ios and further investigate the cascading augmen- tation, we perform extensive ablation studies con- ducted on the 96Music and 96Audio datasets under the 16-99 kHz SR setting (see Fig. 4. Specifically,
2.2
Audio (96 kHzz)
2.026
Music (96 kHzz)
8800
1,458
1.455
1.6
1,361
1.377
1.411
we ablate the following components: (1) dataset filter- ing by removing samples with original sampling rates below kHz, (ii) input/output Biequency-awareneer (iii) waveform-domale filtering-basee augmentation, (iv) latent-space blurring-basd based augmentation, and (v) the effect of dynamically sampled blurring ratios dur- ing training. Across both datasets, each component consistently contributes to performance improvement, as reflected in the overrall LSD. While the dynamic blur ratio provides additional gains, it also offers the flexibility to support both the cascaded SR pipeline and the standalone 48 99 kHz setting, where distortion degradation needs be applied to the input signal. The SR experiments under real-world scenarios and a detailed comparison of augmentation parameters provided in the Appendix
1.4-
1.182
1.186
1219
1.29
1.889
1.2-
Ours (96kHz SR)
we Dynamic Blur
wio Latent Aug
Wi Target- Target-Awwro Aavare
Input Aware
wio Waveform Aug
wo Dataseel Filler
Figure 4: Ablation results 96Audio and
96Music in the 16-96 kHz setting.
Case studies. Fig. 5 presents case studies on 8-448HH speech and 16-+192KHz music SR using
zero-shot model. For speech, compare with recent SoTA methods 122 62
32
NU-
Wave demonstrates strong low-frequency preservation but struggles to recover high-frequency components under the challenging 6x upsampling setting. Frepainter and FlowHigh capture the general
contour, yet lack sufficient spectral energy and fine-grained details. AudioSR generates adequate high-frequency content, but often introduces over-boost and undesired artifacts. In contrast, our method achieves detailed full-band reconstruction, maintaining better energy balance across frequency bands. For music, AudioSR fails retain freeueecc consistency due to its spectrogram- based design, leading to spectral mismatches and weak harmonic modeling, In contrast, our method takes advantages of LBM modeling and frequency-awareness techniques to generate full-band audio with high fidelity at 48kHz. Further cascading to 96/192kHz introduces clearer high-free tigh-free detail and harmonic structure, confirming the effectiveness of architecture design and augmentation strategy.

---

5 Conclusion
In this work, we present AudioLBM, a novel audio upsampling system with bridge models in the continuous latent space of audio waveform, modeling the LR-to-HR audio upsampling process with a latent-to-latedss generative framework. By proposing frequency- aware LBMs, we enable the learning of any-to-any upsampling process at the training stage to enlarge training data, thereby enhancing the super-resolution quality. We further present cascaded LBMs, empowering the audio upsampling beyond 48 kHz, and propose the prior augmentation strategies to reduce cascading errors. Comprehensive experimental results demonstrate that our AudioL.BM outperforms previous audio upsampling systems by a large margin across speech, sound effects, and music signals, and enables high-quality upsampling to 96 kHz and 192 kHz for the first time in audio community. In the future, plan to extend our super-resolution approach to additional modalities (e.g. image, video time series), and further generalize it to a broader range of restoration tasks. As with other generative audio models, method may raise concerns about potential misuse, including unauthorized synthesis of speech or music, imitation of artists' vocal identities, and challenges in verifying the authenticity of audio content, which could contribute to misinformation undermine creative labor.
6 Acknowledgements
This work is supported by the National Natural Science Foundation of China (62550004, U24A20342, U25B6003, 92570001).
References
[1] Andrea Agostinelli, Timo I Denk, Zalán Borsos, Jesse Engel, Mauro Verzetti, Antoine Caillon, Qingqing Huang, Aren Jansen, Adam Roberts, Marco Tagliasacchi, et al. Musiclm: Generating music from text. arXiv preprint axXiv:2301.11323 2023.
[2] Yuval Atzmon, Maciej Bala, Yogesh Balaji, Tiffany Cai, Yin Cui, Jiaojiao Fan, Yunhao Ge, Siddharth Gururani, Jacob Huffman, Ronald Isaac, et al. Edify image: High-quality image generation with pixel space laplacian diffusion models. arXiv preprint arXiv:2411.0711 2024.
[3] AudiogenAI. AGC: Audio Generative Compression. agc 2024. Accessed: 2025-05-21.
[4] Fan Bao, Shen Nie, Kaiwen Xue, Yue Cao, Chongxuan Li, Hang Su, and Jun Zhu. All are worth words: A vit backbone for diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 22669 22679, 2023.
[5] Omer Bar-Tal, Lior Yariv, Yaron Lipman, and Tali Dekel. Multidiffusion: Fusing diffusion paths for controlled image generation. 2023.
[6] Rachel M Bittner, Justin Salamon, Mike Tiemey, Matthias Mauch, Chris Cannam, and Juan Pablo Bello. Medleydb: A multitrack dataset for imnotation-intensie mir research. In Ismir, volume 14, pages 155-160. 2014.
[7] Richard Black. Anti-alias filters: the invisible distortion mechanism in digital audio? In Audio Engineering Society Convention. Audio Engineering Society, 1999.
[8] Jens Blauert. Spatial hearing: the psychophysics of human sound localization. MIT press, 1997.
[9] Zalán Borsos, Raphaël Marinier, Damien Vincent, Eugene Kharitonov, Olivier Pietquin, Matt Sharifi, Dominik Roblek, Olivier Teboul, David Grangier, Marco Tagliasacchi, et al. Audiolm: a language modeling approach to audio generation. IEEE/ACM transactions on audio, speech, and language processing, 31:2523 -2333322533, 2023.
[10] Jianrui Cai, Hui Zeng, Hongwei Yong. Zisheng Cao, and Lei Zhang. Toward real-world single image super-resolution: A new benchmark and a new model. In Proceedings of the IEFF/VVF international conference on computer vision, pages 3086-3095, 2019.
10

---

[11] Clément Chadebec, Onur Tasar, Sanjeev Sreetharan, and Benjamin Aubin. Lbm: Latent bridge matching for fast image-to-image translation. arXiv preprint 7XXi:2503.075335 2025.
[12] Junsong Chen, Chongjian Ge, Enze Xie, Yue Wu, Lewei Yao, Xiaozhe Ren, Zhongdao Wang, Ping Luo, Huchuan Lu, and Zhenguo Li. Pixart-o: Weak-to-strong training of diffusion transformer for 4k text-to-image generation. In European Conference on Computer Vision, pages 74-91. Springer, 2024.
[13] Tiamrong Chen, Horng Liu, and Evangelos A Theodorou. Likelihood training of schr odinger bridge using barkwrdd sdes theory. arXiv preprint 21X1::2110.11911, 2021.
[14] Zehua Chen, Guande He, Kaiwen Zheng, Xu Tan, and Jun Zhu. Schrodinger bridges beat diffusion models on texe-to-speech synthesis. arXiv preprint arXiv:23/2.0349) 2023.
[15] Michael Chinen, Felicia SC Lim, Jan Skoglund, Nikita Gureev, Feargus O'Gorman, and Andrew Hines. Visqol v3: An open source production ready objective speech and audio metric. In International Conference on Quality of Multimedia Experience, pages 1-6. IEEE, 2020.
[16] Youngwoo Cho, Minwook Chang, Gerard Jounghyun Kim, and Jaegul Choo. Progressive upsampling audio synthesis via effective adversarial training.
[17] Hyungjin Chung, Byeongsu Sim, Dohoon Ryu, and Jong Chul Ye. Improving diffusion models for inverse problems using manifold constraints. Advances in Neural Information Processing Systems, 35:25683 25696,,2666622 2022.
[18] Hyungjin Chung, Jeongsol Kim, and Jong Chul Ye. Direct diffusion bridge using data consistency for inverse problems. Advances in Neural Information Processing Systems, 36: 7158-7169, 2023.
[19] Marco Comunita, Zhi Zhong, Akira Takahashi, Shiqi Yang. Mengjie Zhao, Koichi Saito, Yukara lkemiya, Takashi Shibuya, Shusuke Takahashi, and Yuki Mitsufuji. Specmaskgit: Masked generative modelling of audio spectrogram for efficient audio synthesis and beyond.
[20] Yusheng Dai, Chenxi Wang, Chang Li, Chen Wang, Jun Du, Kewei Li, Ruoyu Wang, Jiefeng Ma, Lei Sun, and Jianqing Gao. Latent swap joint diffusion for long- form audio generation. arXiv e-prints, pages arXiv-2502, 2025.
[21] Alexandre Défossez, Jade Copet, Gabriel Synnaeve, and Yossi Adi. High fidelity neural audio compression. arXiv preprint arXiv:2210. 13438, 2022.
[22] Prafulla Dhariwal and Alexander Nichol. Diffusion models beat gans on image synthesis. Advances in Neural Information Processing Systems, 34:8780-8777 -7984, 2021.
[23] Prafulla Dhariwal, Heewoo Jun, Christine Payne, Jong Wook Kim, Alec Radford, and Ilya Sutskever. Jukebox: A generative model for music. arXiv preprint wrXiv:2005.0034/ 2020.
[24] Zhihao Du, Yuxuan Wang, Qian Chen, Xian Shi, Xiang Lv, Tianyu Zhao, Zhifu Gao, Yexin Yang, Changfeng Gao, Hui Wang, et al. Cosyvoice 2: Scalable streaming speech synthesis with large language models. arXiv preprint arXiv:2412.10111 2024.
[25] Adoram Erell and Mitch Weintraub. Estimation using log-spectral-distane criterion for noise- robust speech recognition. In International Conference on Acoustics, Speech, and Signal Processing, pages 853-856, IEEE, 1990.
[26] Zach Evans, Julian Parker, CJ Carr, Zachary Zuckowski, Josiah Taylor, and Jordi Pons. Long-form music generation with latent diffusion.
[27] Zach Evans, CJ Carr, Josiah Taylor, Scott H Hawley, and Jordi Pons. Fast timing- conditooed latent audio diffusion. In Forty-first International Conference on Machine Learning, 2024.
[28] Zach Evans, Julian D Parker, CJ Carr, Zack Zukowski, Josiah Taylor, and Jordi Pons. Stable audio open. ICASSP 2025-2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 1-5. IEEE, 2025.
11

---

[29] Eduardo Fonseca, Xavier Favory, Jordi Pons, Frederic Font, and Xavier Serr.. Fsd50k: an open dataset of human-labeled sound events. /EEE/ACM Transactions on Audio, Speech, and Language Processing. 30:829-852, 2021.
[30] Christian Füllgrabe, Thomas Baer, Michael A Stone, and Brian CJ Moore. Preliminary evaluation of a method for fitting hearing aids with extended bandwidth. International Journal of Audiology, 49(10))741-753 2010.
[31] Jiatao Gu, Shuangfei Zhai, Yizhe Zhang, Joshua M Susskind, and Navdeep Jaitly. Matryoshka diffusion models. The Twelfth International Conference on Learning Representations, 2023.
[32] Seungu Han and Junhyeok Lee. Nu-wave 2: A general neural audio upsampling model for various sampling rates. arXiv preprint arXiv:2206.0854) 2022.
[33] Eric Harper, Somshubra Majumdar, Oleksii Kuchaiev, Li Jason, Yang Zhang, Evelina Bakhturina, Vahid Noroozi, Sandcep Subramanian, Koluguri Nithin, Huang Jocelyn, Fei Jia, Jagadeesh Balam, Xuesong Yang, Micha Livne, Yi Dong, Sean Naren, and Boris Ginsburg. NeMo: a toolkit for Conversational AI and Large Language Models. URL https://github. com/ NVIMDD/MIAA
[34] Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in Neural Information Processing Systems, 33:6840-660 6416840-681,, 2020.
[35] Jonathan Ho, Chitwan Saharia, William Chan, David J Fleet, Mohammad Norouzi, and Tim Salimans. Cascaded diffusion models for high fidelity image generation. Journal of Machine Learning Research, 23(47):1-33, 2022.
[36] Qingging Huang, Daniel S Park, Tao Wang, Timo Denk, Andy Ly. Nanxin Chen, Zhengdong Zhang, Zhishuai Zhang, Jiahui Yu, Christian Frank, et al. Noise2music: Text-conditioned music generation with diffusion models. arXiv preprint wxXiv:2302.03917 2023.
[37] Jaekwon Im and Juhan Nam. Flashsr: One-step versatile audio super-resolution via diffusion distillation. arXiv preprint arXiv:2501. 2025.
[38] Haorui Ji, Taojun Lin, and Hongdong Li. Dpbridge: Latent diffusion bridge for dense prediction. arXiv preprint arXiv:2412.20506 2024.
[39] Yuxuan Jiang, Zehua Chen, Zeqian Ju, Chang Li, Weibei Dou, and Jun Zhu. Freeaudio: Training-free timing planning for controllable long-form text-to-audio generation. arXiv preprint 2xXXi:2507.08555 2025.
[40] Chris Dongjoo Kim, Byeongchang Kim, Hyunmin Lee, and Gunhee Kim. Audiocaps: Gen- erating captions for audios in the wild. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computationnl Linguistics: Human Language Tech- nologies, Volume I (Long and Short Papers), pages 119-132, 2019.
[41] Seung- -oing-Bin Kim, Sang-Hou Hoon Lee, Ha- Yeong Choi, and Seong Whan Lee. Audio super- resolution with robust speech representation learning of masked autoencoder. IEEE/ACM Transactions on Audio, Speech, and Language Processing, 12:1012- 2024.
[42] Diederik P Kingma, Max Welling, et al. Auto-encoding variational bayes, 2013.
[43] Oddur Kjartansson, Supheakmungkol Sarin, Knot Pipatsrisawat, Martin Jansche, and Linne Ha. Crowd-sourced speech corpora for javanese, sundanese, sinhala, nepali, and bangladeshi bengali. In SI.TU, pages 52-55, 2018.
[44] Zhifeng Kong, Wei Ping, Jiaji Huang, Kexin Zhao, and Bryan Catanzaro. Diffwave: A versatile diffusion model for audio synthesis. arXiv preprint arXiv:2009.09761, 2020.
[45] Zhifeng Kong, Kevin J Shib, Weili Nie, Arash Vahdat, Sang-gil Lee, Joao Felipe Santos, Ante Jukie, Rafael Valle, and Bryan Catanzaro. A2sb: Audio-to-audio schrodinger bridges. arXiv preprint arxiv:2501.11311. 2025.
12

---

[46] Pin-Jui Ku, Alexander H Liu, Roman Korostik, Sung-Feng Huang, Szu-Wei Fu, and Ante Jukié. Generative speech foundation model pretraining for high-quality speech extraction and restoration. In IEFE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 1-5. IEFE,, 2025.
[47] Volodymyr Kuleshov, Zayd Enam, and Stefano Ermon. Audio super resolution using neural networks. arXiv preprint /00i::7708.00853 2017.
[48] Rithesh Kumar, Prem Seetharaman, Alejandro Luebs, Ishaan Kumar, and Kundan Kumar. High-fidelity audio compression with improved rvqgan. Advances in Neural Information Processing Systems, (16227800-27992 2023.
[49] Junhyeok Lee and Seungu Han. Nu-wave: A diffusion probabilistic model for neural audio upsampling. arXiv preprint arXiv:2104.02321, 2021.
[50] Sang gil Lee, Zhifeng Kong, Arushi Goel, Sungwon Kim, Rafael Valle, and Bryan Catanzaro. Etta: Elucidating the design space of text-to-audio models. arXiv preprint 1rXi5:2412.19351, 2024.
[51] Yongjoon Lee and Chanwoo Kim. Wave-u-mamba: an end-to-end framework for high-quality and efficient speech super resolution. In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 1-5, IEEE, 2025.
[52] Bo Li, Kaitao Xue, Bin Liu, and Yu-Kun Kun Lai. Bbdm: Image-to-image translation with brownian bridge diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1952-1961, 2023.
[53] Chang Li, Ruoyu Wang, Lijuan Liu, Jun Du, Yixuan Sun, Zilu Guo, Zhenrong Zhang, Yuan Jiang, Jianqing Gao, and Feng Ma. Quality-aware masked diffusion transformer for enhanced music generation. arXiv preprint arXiv:2405.1588
2024.
[54] Chang Li, Zehua Chen, Fan Bao, and Jun Zhu. Bridge-sr: Schrödinger bridge for efficient In ICASSP 2025-2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 1-5, IEEE, 2025.
[55] Kai Li and Yi Luo. Apollo: Band-sequence modeling for high-quality audio restoration. In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 1-5. IEEE, 2025.
[56] Teck Yian Lim, Raymond A Yeh, Yijia Xu, Minh N Do, and Mark Hasegawa-Johnson. Time- frequency networks for audio super-resolution. In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 646-650. IEEE, 2018
[57] Martin Link. Digital audio at 96 khz sampling frequency-pros and cons of new audio technique. In Audio Engineering Society Convention. Audio Engineering Society, 1999.
[58] Guan-Horng Liu, Arash Vahdat, De-An Huang, Evangelos A Theodorou, Weili Nie, and Anima Anandkumar. 12sb: image-to-image schrödinger bridge. In Proceedings of the 40th International Conference on Machine Learning, pages 220622 2023.
[59] Haohe Liu, Qiuqiang Kong, Qiao Tian, Yan Zhao, DeLiang Wang. Chuanzeng Huang, and Yuxuan Wang. Voicefixer: Toward general speech restoration with neural vocoder. arXiv preprint 2xXv:2119913331, 2021.
[60] Haohe Liu, Woosung Choi, Xubo Liu, Qiuqiang Kong, Qiao Tian, and DeLiang Wang. Neural vocoder is all you need for speech super-resolution. arXiv preprint arXiv:2203. 14941, 2022.
[61] Haohe Liu, Zehua Chen, Yi Yuan, Xinhao Mci, Xubo Liu, Danilo Mandic, Wenwu Wang. and Mark D Plumbley. Audioldm: text-to-audio generation with latent diffusion models. In Proceedings of the 40th International Conference on Machine Learning, pages 21450-21474, 2023.
[62] Haohe Liu, Ke Chen, Qiao Tian, Wenwu Wang, and Mark D Plumbley. Audiosr: Versatile audio super-resolution at scale. In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 1076-1080. IEEE, 2024.
13

---

[63] Haohe Liu, Yi Yuan, Xubo Liu, Xinhao Mei, Qiuqiang Kong, Qiao Tian, Yuping Wang, Wenwu Wang, Yuxuan Wang, and Mark Plumbley. Audioldm 2: Learning holistic audio generation with self-supervised pretraining. IEEF/ACM Transactions on Audio, Speech, and Language Processing, 2024.
[64] Xingchao Liu and Lemeng Wu. Learning diffusion bridges on constrained domains. In International Conference on Learning Representations, 2023.
[65] Ye-Xin Lu, Yang Ai, Hui-Peng Du, and Zhen-Hua Ling. Towards high-quality and effi- cient speech bandwidth extension with parallel amplitude and phase prediction. IEEE/ACM Transactions on Audio, Speech, and Language Processing, 2024.
[66] Ye-Xin Lu, Yang Ai, Zheng-Yan Yan Sheng, and Zhen-Hua Ling, Multi-stage speech bandwidth extension with flexible sampling rate control. arXiv preprini arXiv:2406.022330 2024.
[67] Andreas Lugmayr, Martin Danelljan, Andres Romero, Fisher Yu, Radu Timofte, and Luc Van Gool. Repaint: Inpainting using denoising diffusion probabilistic models. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 11461-1177,, 2022.
[68] Ilaria Manco, Benno Weck, Seungheon Doh, Minz Won, Yixiao Zhang, Dmitry Bogdanov, Yusong Wu, Ke Chen, Philip Tovstogan, Emmanouil Benetos, et al. The song describer dataset: corpus of audio captions for music-and-language evaluation. In Workshop on Machine Learning for Audio, Neural Information Processing Systems (NeurIPS). Neural Information Processing Systems, 2023.
[69] Moshe Mandel, Or Tal, and Yossi Adi. Aero: Audio super resolution in the spectral domain. In IEEE International Conference Acoustics, Speech and Signal Processing (ICASSP), pages 1-5. IEEE, 2023.
[70] Brian McFee, Colin Raffel, Dawen Liang, Daniel PW Ellis, Matt Mc Eric Battenberg, and Oriol Nieto. librosa: Audio and music signal analysis in python. SciPy, 2015:18 10:::8-222 24, 2015.
[71] Eloi Moliner and Vesa Välimäki. Behm-gan: Bandwidth extension of historical music using generative adversarial networks. IEEE/ACM Transactions on Audio, Speech, and Language Processing, 31:943-955 956, 2022.
[72] Eloi Moliner, Jaakko Lehtinen, and Vesa Välimäki. Solving audio inverse problems with diffusion model. In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 1 1-5. IEEE, 2023.
[73] Eloi Moliner, Filip Elvander, and Vesa Välimäki. Blind audio bandwidth extension: A diffusion-basee zero-shot approach. IEEE/ACM Transactions on Audio, Speech, and Language Processing, 2024.
[74] Eloi Moliner, Maija Turunen, Filip Elvander, and Vesa Välimäki. A diffusion- based generative equalizer for music restoration. arXiv preprint arXiv:2403. 18636, 2024.
[75] Tu Anh Nguyen, Wei-Ning Hsu, Antony d' Avirro, Bowen Shi, Itai Gat, Maryam Fazel-Zarani, Tal Remez, Jade Copet, Gabriel Synnaeve, Michael Hassid, et al. Expresso: A benchmark and analysis of discrete expressive speech resynthesis. arXiv preprint arXiv:2308.05725, 2023.
[76] Viet-Anh Nguyen, Anh HT Nguyen, and Andy WH Khong. Tunet: A block-online bandwidth extension model based on transformers and self-supervised pretraining. In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 161-165. IEEE, 2022.
[77] Vassil Panayotov, Guoguo Chen, Daniel Povey, and Sanjeev Khudanpur. Librispeech: asr corpus based on public domain audio books. In 20/5 IEEE international conference on acoustics, speech and signal processing (ICASSP), pages 5206-5210. IEEE, 2015.
[78] William Peebles and Saining Xie. Scalable diffusion models with transformers. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 4195-4205, 2023.
14

---

[79] Karol J Piczak. Esc: Dataset for environmental sound classification. In Proceedings of the 23rd ACM international conference on Multimedia, pages 1015-1018, 2015.
[80] Dustin Podell, Zion English, Kyle Lacey, Andreas Blattmann, Tim Dockhorn, Jonas Müller, Joe Penna, and Robin Rombach. Sdxl: Improving latent diffusion models for high-resolution image synthesis. arXiv preprint arXiv:2307.01952. 2023.
[81] KR Prajwal, Bowen Shi, Matthew Lee, Apoorv Vyas, Andros Tjandra, Mahi Luthra, Baishan Guo, Huiyu Wang, Triantafyllos Afouras, David Kant, et al. Musicflow: Cascaded flow matching for text guided music generation. arXiv preprint arXiv:2410.20477 2024.
[82] Zafar Rafii, Antoine Liutkus, Fabian-Robert Stöter, Stylianos loannis Mimilakis, and Rachel Bittner. The musdb18 18 corpus for music separation. 2017.
[83] Aditya Ramesh, Prafulla Dhariwal, Alex Nichol, Casey Chu, and Mark Chen. Hierarchical text-conditional image generation with clip latents. arXiv preprint arXiv:2204.06125, 1(2):3
2022.
[84] Chandan KA Reddy, Harishchandra Dubey, Kazuhito Koishida, Arun Nair, Vishak Gopal, Ross Cutler, Sebastian Braun, Hannes Gamper, Robert Aichner, and Sriram Srinivasan. Interspeech 2021 deep noise suppression challenge. arXiv preprint arXiv:2101.01900 2021.
[85] Joshua D Reiss. A meta-analysis of high resolution audio perceptual evaluation. Journal of the Audio Engineering Society, 2016.
[86] Julius Richter, Simon Welker, Jean-Marie Lemercier, Bunlong Lay, and Timo Gerkmann. Speech enhancement and dereverberation with diffusion-based generative models. JEEE/ACM Transactions Audio, Speech, and Language Processing, 11:2351-2364 2023.
[87] Nicolae-Cätälin Ristea, Babak Naderi, Ando Saabas, Ross Cutler, Sehastian Braun, and Solomiya Branets. Icassp 2024 speech signal improvement challenge. IEEE Open Journal of Signal Processing, 2025.
[88] Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Bjöm Ommer. High-resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 10684-10695, 2022.
[89] Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U-net: Convolutional networks for biomedical image segmentation. In Medical Image Computing and Computer-Assisted Inter- vention, pages 234-241. Springer, 2015.
[90] Chitwan Saharia, William Chan, Saurabh Saxena, Lala Li, Jay Whang, Emily L Denton, Kamyar Ghasemipour, Raphael Gontijo Lopes, Burcu Karagol Ayan, Tim Salimans, et al. Photorealistic text-to-image diffusion models with deep language understanding. Advances in neural information processing systems, 35:36479-36499 2022.
[91] Chitwan Saharia, Jonathan Ho, William Chan, Tim Salimans, David J Fleet, and Mohammad Norouzi. Image rusertresolution via iterative refinement. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(4):4713 4726, 2022.
[92] Robin San Roman, Yossi Adi, Antoine Deleforge, Romain Serizel, Gabriel Synnaeve, and Alexandre Défossez. From discrete tokens to high-fidelity audio using multi-band diffusion. Advances in Neural Information Processing Systems, 36: 36:1522-1538. 2023.
[93] Flavio Schneider, Ojasv Kamal, Zhijing Jin, and Bernhard Schölkopf. Moûsai: Efficient text-to-music diffusion models. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 8050-8068, 2024.
[94] Erwin Schrödinger. Sur la théorie relativiste de l'électron et I' I'interpéétation de mécanique quantique. In Annales de I' l'institut Henri Poincaré, volume 2, pages 269-310, 1932.
[95] Johannes Schusterbauer, Ming Gui, Pingchuan Ma, Nick Stracke, Stefan Andreas Baumann, Vincent Tao Hu, and Björ Ommer. Fmboost: Boosting latent diffusion with flow matching. In European Conference on Computer Vision, pages 338-355. Springer, 2024.
15

---

[96] Chenhao Shuai, Chaohua Shi, Lu Gan, and Hongqing Liu. mdctgan: Taming transformer-based gan for speech super-resolution with modified det spectra. arXiv preprint arXiv:2305.11104 2023.
[97] Ivan Skorokhodov, Sharath Girish, Benran Hu, Willi Menapace, Yanyu Li, Rameen Abdal, Sergey Tulyakov, and Aliaksandr Siarohin. Improving the diffusability of autoencoders. arXiv preprint arXiv:2502. 14831, 2025.
[98] Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-based generative modeling through stochastic differential equations. arXiv preprint arXiv:2011.13456. 2020.
[99] Christian J Steimmetz and Joshua D Reiss. auraloss: Audio focused loss functions in pytorch. In Digital music research network one-day workshop (DMRN+ 15), 2020.
[100] Christian Steinmetz, Jordi Pons, Santiago Pascual, and Joan Serrà. Automatic multitrack mixing with differentiable mixing console of neural audio effects. In ICASSP 2021-2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 71-75. IEEE, 2021.
[101] Robert Stuart. Coding high quality digital audio. Japan Audio Society, 1997.
[102] Jiaqi Su, Yunyun Wang, Adam Finkelstein, and Zeyu Jin. Bandwidth extension is all you need. In ICASSP 2021-2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 696-700. IEEE, 2021.
[103] Xuan Su, Jiaming Song, Chenlin Meng, and Stefano Ermon. Dual diffusion implicit bridges for image-to-image translation. arXiv preprint arXiv:2203.08382, 2022.
[104) Jiayan Teng, Wendi Zheng. Ming Ding, Wenyi Hong, Jianqiao Wangni, Zhuoyi Yang, and Jie Tang. Relay diffusion: Unifying diffusion process across resolutions for image synthesis. arXiv preprint 230.:2330000335000 2023.
[105] Qiao Tian, Yi Chen, Zewang Zhang, Heng Lu, Linghui Chen, Lei Xie, and Shan Liu. Tfgan: Time and frequency domain based generative adversarial network for high-fidelity speech synthesis. arXiv preprint arXiv:2011.12200 2020.
[106] Aaron Van Den Oord, Sander Dieleman, Heiga Zen, Karen Simonyan, Oriol Vinyals, Alex Graves, Nal Kalchbrenner, Andrew Senior, Koray Kavukcuoglu, et al. Wavenet: A generative model for raw audio. arXiv preprint arXiv:1609.03444 12, 2016.
[107] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin, Attention is all you need. Advances in Neural Information Processing Systems, 30, 2017.
[108) Gefei Wang, Yuling Jiao, Qian Xu, Yang Wang, and Can Yang. Deep generative learning via schrödinger bridge. In International Conference on Machine Learning, pages 10794-10804. PMLR, 2021.
[109] Heming Wang and DeLiang Wang. Towards robust speech super-resolution. JEEE/ACM Transactions on Audio, Speech, and Language Processing, 29:2058-2066
2021.
[110] Yuancheng Wang, Zeqian Ju, Xu Tan, Lei He, Zhizheng Wu, Jiang Bian, et al. Audit: Audio editing by following instructions with latent diffusion models. Advances in Neural Information Processing Systems, 16:71340-71357, 2023.
[111] Yuancheng Wang. Haoyue Zhan, Liwei Liu, Ruihong Zeng. Haotian Guo, Jiachen Zheng, Qiang Zhang, Xueyao Zhang, Shunsi Zhang, and Zhizheng Wu. Maskget: Zero-shot text-to- speech with masked generative codec transformer. arXiv preprint mrXiv:2409.0075:0 2024.
[112] Zhifeng Wang, Diqun Yan, Rangding Wang, Li Xiang, and Tingting Wu. Speech resampling detection based on inconsistency of band energy. Computers, Materials & Continua, 56(2), 2018.
16

---

[113] Zhou Wang, Alan C Bovik, Hamid R Sheikh, and Eero P Simoncelli. Image quality assessment: from error visibility to structural similarity. IEEE Transactions on Image Processing. 13(4): 600-612, 2004.
[114] Simon Welker, Matthew Le, Ricky TQ Chen, Wei-Ning Hsu, Timo Gerkmann, Alexander Richard, and Yi-Chiao Wu. Flowdec: A flow-based full-band general audio codec with high perceptual quality, arXiv preprini 25Xiv:2503.01455 2025.
[115] Yi-Chiao Wu, Israel D Gebru, Dejan Marković, and Alexander Richard. Audiodec: An open- source streaming high-fidelity neural audio codec. In ICASSP 2023-2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 1-5. IEEE, 2023.
[116] Enze Xie, Junsong Chen, Junyu Chen, Han Cai, Haotian Tang, Yujun Lin, Zhekai Zhang, Muyang Li, Ligeng Zhu, Yao Lu, al. Sana: Efficient high-resolution image synthesis with linear diffusion transformers. arXiv preprint arXiv:2410. 10629, 2024.
[117] Wanghan Xu, Xiaoyu Yue, Zidong Wang, Yao Teng, Wenlong Zhang, Xihui Liu, Luping Zhou, Wanli Ouyang, and Lei Bai. Exploring representation-alignee latent space for better generation. arXiv preprint arXiv:2502.00355 2025.
[118] Junichi Yamagishi, Christophe Veaux, Kirsten MacDonald, al. Cstr vetk corpus: English multi-speaker corpus for cstr voice cloning toolkit (version 0.92). University of Edinburgh. The Centre for Speech Technology Research (CSTR), pages 271-350, 2019.
[119] Zhuoyi Yang. Heyang Jiang, Wenyi Hong, Jiayan Teng, Wendi Zheng, Yuxiao Dong, Ming Ding, and Jie Tang, Inf-dit: Upsampling any-resolution image with memory-efficcint diffusion transformer. In European Conference on Computer Vision, pages 141-156. Springer, 2024.
[120] Chin- Yun Yu, Sung-Lin Yeh, György Fazekas, and Hao Tang. Conditioning and sampling in variational diffusion models for speech super-resolution. In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 1-5. IEEE, 2023.
[121] Ruibin Yuan, Hanfeng Lin, Shuyue Guo, Ge Zhang, Jiahao Pan, Yongyi Zang, Haohe Liu, Yiming Liang Wenye Ma, Xingjian Du, et al. Yue: Scaling open foundation models for long-form music generation. arXiv preprint arXiv:2503.08638 2025.
[122] Jun-Hak Yun, Seung-Bin Kim, and Scong-Whai Lee. Flowhigh: Towards efficient and high-quality audio super-resolution with single-step flow matching. arXiv preprint arXiv:250I. XXiv:2501.04926, 2025.
[123] Chong Zhang. Yukun Ma, Qian Chen, Wen Wang, Shengkui Zhao, Zexu Pan, Hao Wang, Chongjia Ni, Trung Hieu Nguyen, Kun Zhou, et al. Inspiremusic: Integrating super resolution and large language model for high-fidelity long-form music generation. arXiv preprint arXiv:2503.0000 2025.
[124] Kai Zhang, Jingyun Liang, Lue Van Gool, and Radu Timofte. Designing a practical degradation model for deep blind image super-resolution In Proceedings of the IEEE/CVF international conference on computer vision, pages 48000, 2021.
[125] Kexun Zhang, Yi Ren, Changliang Xu, and Zhou Zhao. Wsrglow: A glow-based waveform generative model for audio super-resolution. arXiv preprint 10Xiv:2106.08507, 2021.
[126] Ting-Wer Wei Zhang and Shanq-Jang Ruan. Vm-asr: lightweight dual-stream u-net model for efficient audio super-resolution. IEEE Transactions on Audio, Speech and Language Processing, 2025.
[127] Wendi Zheng, Jiayan Teng, Zhuoyi Yang, Weihan Wang, Jidong Chen, Xiaotao Gu, Yuxiao Dong, Ming Ding, and Jie Tang. Cogview3: Finer and faster text-to-image generation via relay diffusion. In European Conference on Computer Vision, pages 1 1-22. Springer, 2024.
[128] Kanglei Zhou, Zikai Hao, Liyuan Wang, and Xiaohui Liang. Adaptive score alignment learning for continual perceptual quality assessment of 360-degree videos in virtual reality. IEEE Transactions on Visualization and Computer Graphics, (155)228802890 2025.
17

---

[129] Kanglei Zhou, Hubert P. H. Shum, Frederick W. B. Li, Xingxing Zhang, and Xiaohui Liang. Phi: Bridging domain shift in long-term action quality assessment progressive hierarchical instruction. IEEE Transactions on Image Processing, 34:3718-3732, 2025. ISSN 1057-7149.
doi: 10.1 10.110/91.22003354441...
[130] Linqi Zhou, Aaron Lou, Samar Khanna, and Stefano Ermon. Denoising diffusion bridge models. arXiv preprint 2009.18309.,6448, 2023.
[131] Ge Zhu, Juan-Pablo Caceres, Zhiyao Duan, and Nicholas J Bryan. Musichifi: Fast high-fidelity stereo vocoding. IEEE Signal Processing Letters, 2024.
18

---

NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: We confirm that the main claims made in the abstract and introduction accu- rately reflect the paper's contributions and scope.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or
NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
is fine to include aspirational goals as motivation as long as is clear that these goals not attained by the paper.
2. Limitations
Question: Does the paper discuss the limitations the work performed by the authors?
Answer: [Yes]
Justification:
The paper has discussed the limitations of the work, see Sec, 5.
Guidelines:
The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create a separate "Limitations" section their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution is low images are taken in low lighting. Or speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.
While the authors might fear that complete honesty about limitations might used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't 't acknowledged judgment and recognize that individual actions in favor of transparency play impor- tant role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
the paper. The authors should use their best
3. Theory assumptions and proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
Answer: [NA]
19

---

Justification:
The paper does not include theoretical results.
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced the statement of any theorems.
The proofs can either appear the main paper or the supplemental material, but they appear in the supplemental material, the authors are encouraged to provide short proof sketch to provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental result reproducibility
Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
Question:
Answer: [Yes]
Justification: The authors have described necessary information to reproduce the main experimental results of the paper, Sec. 4.
Guidelines:
The answer NA means that the paper does include experiments. If the paper includes experiments, No answer this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g.. in the case of large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
While NeurIPS does not require releasing code, the conference does require all submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) If the contribution is primarily a new algorithm, the paper should make it clear how reproduce that algorithm. (b) If the contribution is primarily
model architecture, the paper should describe the architecture clearly and fully.
(c) If the contribution is a new model (e.g., a large language model), then there should either be way to access this model for reproducing the results or way to reproduce the model (e.g., with an open-source dataset instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome deseribe the particular way they provide for reproducibility, In the case of closed-source models, it may be that access to the model is limited in some way (e.g., registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.
5. Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material?
20

---

Answer: [NA]
Justification: The authors will provide detailed implementation specifics in the supplemen- tary materials, but the code is not available at this stage.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurIPS code and data submission guidelines (https://nips. cc/
for more details.
While we encourage the release of code and data, we understand that this might not be possible, so "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for new open-source benchmark).
The instructions should contain the exact command and environment needed to to reproduce the results. See the NeurlPS code and data submission guidelines (https
hetpolliiiggiddee/ooooooo /oaeeeeee/oooubbbibiaoo ssionpolicy) for more details.
The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. only subset of experiments are reproducible, they should state which ones are omitted from the script and why.
At submission time, preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible in supplemental material (appended to the paper) recommended, but including URLs to data and code permitted.
6. Experimental setting/details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
Justification: The paper has specified all the training and test details necessary understand the results, see Sec. 4.
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, appendix, as supplemental material.
7. Experiment statistical significance
Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Question:
Answer: [No]
Justification:
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results are accompanied by error bars, confi- dence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.
The factors of variability that the error bars capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall with given experimental conditions).
The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)
The assumptions made should be given (e.g., Normally distributed errors).
21

---

It should be clear whether the error bar is the standard deviation or the standard error of the mean.
OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality errors is not verified.
For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that out of range (e.g. negative error rates).
If error bars are reported in tables or plots, The authors should explain the text how they were calculated and reference the corresponding figures tables in the text.
8. Experiments compute resources
For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed reproduce the experiments?
Question:
Answer: [Yes]
Justification: The paper has provided sufficient information the computer resources, Section 4.1.
Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.
The paper should provide the amount compute required for each of the individual experimental runs well estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't It make it into the paper).
9. Code of ethics
Question: Does the research conducted the paper conform, in every respect, with the NeurlPS Code of Ethics
The research conducted in the paper conforms with the NeurIPS Code of Answer: [Yes]
Justification:
Ethics.
Guidelines:
The answer NA means that the authors have reviewed the NeurIPS Code of Ethics.
If the authors answer No, they should explain the special circumstances that require deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g., if there is special consid- eration due to laws or regulations their jurisdiction).
10. Broader impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [Yes]
Justification: The authors have discussed the broader impacts of this paper, see Section Guidelines.
Guidelines:
The answer NA means that there is no societal impact of the work performed.
If the authors answer NA or No. they should explain why their work has no societal impact or why the paper does not address societal impact.
Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
22

---

The conference expects that many papers will be foundational research and not tied particular applications, let alone deployments. However, if there is direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology being used intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.
If there negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms monitor how system learns from feedback over time, improving the efficiency and accessibility of MI..
11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data models that have high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [NA]
Justification:
The paper does not pose such risks.
Guidelines:
The answer NA means that the paper poses such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Lieenses for existing assets
Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper. properly credited and are the license and terms of use explicitly mentioned and properly respected?
Answer: [NA]
Justification: The paper does not pose such risks.
Guidelines:
The answer NA means that the paper does existing assets.
The authors should cite the original paper that produced the code package or dataset.
The authors should state which version of the asset is used and, if possible, include URL.
The name of the license (c.g., CC-BY 4.0) should be included for each asset.
For scraped data from a particular source (c.g., website), the copyright and terms of service of that source should be provided.
If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswi thcode. com com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.
23

---

If this information is not available online, the authors are encouraged to reach out to the asset's creators.
13. New assets
Question: Are assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [Yes]
The creators or original owners assets (e.g., code, data, models), used in the paper, properly credited and only permissively licensed data are selected the train model.
Justification:
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details the dataset/code/moodl as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent was obtained from people whose asset used.
At submission time, remember to anonymize your assets (if applicable). You can either create anonymized URL include anonymized zip file.
14. Crowdsourcing and research with human subjects
For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and sereenshots, if applicable, as well details about compensation (if any)?
Question:
Answer: [NA]
Justification:
The paper does not release new assets
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Including this information the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then much detail as possible should be included the main paper.
According to the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional review board (IRB) approvals or equivalent for research with human subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or equivalent approval/teview based the requirements of your country or institution) were obtained?
Answer: [Yes]
Justification: TThe authors provide detailed descriptions of the subjective evaluation setup in the Appendix G.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere the NeurIPS Code of Ethics and the guidelines for their institution.
24

---

For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.
16. Declaration of LLM usage
Question: Does the paper describe the usage of LLMs if it is important, original, or non-standard component of the core methods in this research? Note that the LLM is used only for writing, editing, formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.
Answer: [NA]
Justification: The paper does not suffer these risks.
Guidelines:
The answer NA means that the core method development in this research does not involve LLMs as any important, original, non -tandtaddrrd components.
Please refer to our LLM policy for what should or should not be described.
25

---

Appendix
A
Data processing
A.1 Selecting ftaget in any-to-any training paradigm
Our any-to-any training strategy adopts a flexible target sampling rate furget. where the input rate is randomly sampled fprior ~ U ([min= furget). While this design improves generalization and robust- ness, it may also suffer from the presence of unexpected distortion, device artifacts, or environmental noise in high-frequener regions [84]. which frequently occur in in-the-wild recordings. As result, training SR models with fiurge exceeding the meaningful frequency range may potentially lead to overfitting to compression artifacts or aliasing patterns, rather than learning useful structure. Such failure cases are shown in Figure 6
Bad Case
Case
Figure The impact high-frequency noise on super-resolution outputs. Without an effective choice of furget. the SR model hallucinates unnatural noise and artifacts in the gigh-freuency band.
These hallucinations not only degrade perceptual quality [02 but also propagate errors in subsequent cascade stages. To mitigate this, we restrict training targets to more reliable range by enforcing furget [ITr(z), where (xf denotes the estimated effective bandwidth of input that identifies the
frequency range where signal energy is concentrated 10 124 102
Estimating far- Traditional methods estimate fan(x: using energy- heuristics, such as com- puting the log-ratio of total signal energy before and after low-pass filtering [112), applying spectral roll-off thresholds as implemented in Librosa 770 based on cumulative spectral energy. However, these approaches are often sensitive to broadband or high-frequency noise, which can lead to inaccurate estimates usable bandwidth (see Figure 7 CQT-Diff++ [73] proposes an iterative refinement strategy more accurately approximate the true effective frequency band. However, it requires carefully tuned filtering parameters and introduces additional inference overhead.
To address these issues, we adopt a robust data preprocessing pipeline, shown in Figure g Given raw waveform z, we first estimate the effective cut-off frequency far(()) using curvature-awar spectral analysis, then apply low-pass filter at far(x) to suppress high-freque freh-ffreuency noise and artifacts, effectively boosting the fidelity and stability downstream super-resolution models.
Data preprocessing
99% Roll-off energy frequency estimation
Curvature-aware estimation
Low pass filters
Figure 7: Our proposed data preprocessing pipeline estimates the effective cut-off frequency and removes spectral noise, leading to more suitable samples for SR training.
26

---

141
Cavl Fille
Averaging Downsemping
Savitzkyy Golay Filter
Log
Averaging Downsampting
Figure 8: Overview of our proposed curvature-aware estimation pipeline. Given raw waveform I, we first compute its magnitude spectrum via FFT, followed by Savitzky-Golay smoothing and local downsampling to obtain a denoised spectrum. We then compute the second-order curvature over the log-magnitude spectrum to detect the effective cut-off frequency fan(2), which is used for downstream low-pass filtering. As result, our method is robust to high-frequency noise.
We propose curvature- aware approach to estimate the effective bandwidth far(x) of audio signal, as illustrated in Figure 8 Our key motivation is that informative frequency regions exhibit stronger local variation, while noise silence appears smoother especially in the -aggiitde spectrum.
Given the densely sampled FFT magnitude X(f) = (FFT())())) we apply Savitzky-Gold smooth- ing and downsampling to obtain X,, then define the truncation index i' as the smallest index where local curvature" falls below threshold Cars and spectral energy drops below т:
| log XyI < 6ar and X, <T].
arg min max (E(,.t+A)
(6)
The estimated bandwidth is then:
i* 8r Sett
N
2
During training, low-pass filter each input at for to suppress spurious high-frequency components as data preprocessing, improving stability and perceptual quality in subsequent SR stages.
A.2 Importance of fprior detection for inference
At inference time, (1)) estimated for each input sample with the same detection method of feff individually, allowing adaptive filtering tailored to the true spectral bandwidth of the audio. This ensures that super-resolution performed the informative signal subspace, leading to improved perceptual quality and generalization When generative models are used as the source of input audio, such as MaskGCT [ITI). the nominal output sampling rate is fixed (e.g.. 24 kHz). However, the actual frequency content may vary depending on the speech prompt or training data, and may not occupy the full bandwidth of the input sampling rate. Similar phenomena have also been observed in 16 kHz generation models [61), where the effective bandwidth is often narrower than the nominal sampling rate. Consequently, using the declared sampling rate as the low-pass cutoff for super-resolution input may lead to incorrect reconstruction.
As illustrated in Figure exhibits a clear spectral roll-off well below the Nyquist frequency (12 kHz).
although the model declares 24 kHz sampling rate, its generated waveform
$ log X 1/2 (- log Xita + 16 16log X 30 log X, + 16 log X,-1 log X1-2).
27

---

Input (24 kitz)
Ours (with detected Input frequency)
AudioSR (with inaccurato out frequency)
Figure 9: Super-resolution results for samples generated by MaskGCT [11 at 24 kHz, using both AudioSR and our proposed system. While the nominal sampling rate is 24 kHz, the actual spectral content does not span the full bandwidth. As shown in the result of AudioSR, using 24 kHz directly as the cutoff frequency results in incorrect high-frrquency generation.
Using 12 kHz the cutoff frequency by default leads noticeable spectral discontinuities and artifacts in the output. In contrast, our method first estimates the effective bandwidth the input audio and adjusts the filtering accordingly, thereby avoiding the generation of spurious high- freeufreyencyy content and producing a more natural and coherent spectrum.
B Compression network
Variational autoencoders (VAEs) include an encoder & and a decoder DD The encoder maps an imput æ to a latent representation The training loss is
((x), and the decoder reconstructs æ from via á D(z).
L Ex-xx (R(D(E())),::) (L(ue(=(a))
[I, I)),
(8)
where is reconstruction loss that measures the distance between the original sample æ and the reconstructed sample (xE())). as (= (x) is the approximate posterior distribution over z given æ, and the KL term regularizes this posterior toward standard Gaussian prior.
We follow the similar training network structure and pipeline with Stable-Audoo-Ope Open 28 and ETTA [50], which combines the following training objectives:
1. A multi-resolution STFT loss
999
100
m
[stft stft, stff; +
log stft,()))
1) stft,
CMRSTFT (z. 2)
||stft, (x) |F
2. An adversarial hinge loss and feature matching loss from EnCodec 21
Cadv x) =
[max((, Dx(x)) + max(0, 1.0...+ (x))))
Lrean (2e, at)
KL
mean (x))
where D is the /-th layer of the k-th discriminator Dz-
3. The KI. divergence loss:
(2)x) I)).
B.1 48 kHz compression network
An effective compression network is critical to latent-based super-resolution. However, most existing audio compression models fail to maintain strong reconstruction quality, thereby limiting the upper bound of downstream performance. In this section, analyze the effect of latent compression rate,
28

---

KL divergence, and latent scaling coefficient on both reconstruction and generation. Finally, we also compare our VAE other baselines.
To ensure fair evaluation of both reconstruction and generation capabilities, we train each ablated VAE configuration our full speech corpus (details in Appendix G for 200K steps, and pair it with a corresponding Latent Bridge Model (LBM) trained for 150K steps. All evaluations are conducted on the VCTK-test set. Throughout, we fix the VAE channel dimension to 64 for consistency, we found that a higher channel dimension often leads to unstable training.
B.1.1 Compression rate
Typically, for the generation task, higher compression typically improves generative modeling without significantly compromising reconstruction [26]. However, in low-level tasks such as audio super- resolution, we observe that lower compression rates consistently yield better reconstruction and SR performance, as shown in Table 4 Nevertheless, lower compression introduces longer training time and higher inference cost (RTF), thus reducing deployment efficiency.
To this end, we conduct experiments under fixed L.B training budget (96 A800-hours), and find that compression rate of 512 achieves the best trade-off between efficiency and performance, delivering consistently superior results across both objective and subjective metrics.
Metric/ Compression rate T, 2048
1024
512
256
Reconstruction
SSIM
0.925
0.930
0.946
0.959
LSD4
0.664
0.679
0.665
0.637
SigMOSt
3.099
3,083
3.169
3.142
Generation
SSIMI
0.911
0.912
0.925
0.936
LSD1
0.730
0.714
0.710
0.687
SigMOSt
3.088
3.025
3.139
3.088
Trained in equal time
SSIM
0,900
0.912
0.925
0.905
LSD4
0.730
0.742
0.711
0.825
SigMOSt
3.086
2.958
3.130
3.029
RIF (A800, 100 step)
0.180
0,370
0.700
1.140
Table 4: Objective and subjective evaluation under different compression rates T. Metrics include SSIM, LSD, and SigMOS across reconstruction, generation, and time equalization settings.
B.1.2 KL divergence
For diffusion- generation, increasing the KL divergence term is known to improve the alignment between the latent space and the Gaussian prior, thereby enhancing the diffusability autoencoders and improving generation quality 117 97]. However, in bridge models, the prior distribution no longer a standard Gaussian but instead a Dirac distribution induced by the low-resolution waveform latent. In this setting, enforcing KI. regularization may no longer be appropriate. Moreover, a smaller-or even zero zero-KL. KL weight allows the latent space to prioritize reconstruction fidelity, potentially lifting the upper bound of super-resolution quality. To examine this, Table repporss results under a fixed compression rate of 512, with KL coefficients set to O, Ie-7, 1c-5, 1e-3, Consistent with trends observed in Section B.I.I. we find that smaller KL values (as low 0 or 1e-7) yield better reconstruction and super-resolution performance in the LBM setup- contrasinn with the usual observations in diffusion- based generation tasks.
also observe that reducing the KL weight causes the latent distribution to expand, reflected in significantly increased minimum and maximum values. This can potentially hinder training stability and downstream modeling. To mitigate this, we introduce a simple post-scaling strategy for the latent space. For KL values of (0, le-7, le-5), apply a fixed scaling factor s, chosen such
29

---

Metrie/KL
1e-7
le-5
1e-3
Reconstruction
SSIM
0.942
0.942
0.940
0.935
LSD 1
0,651
0.619
0.637
0.664
pMOS
3.111
3.079
3.103
3.030
mean
0.0506
0.1047
-0.0123
-0.02
std
3,9313
4.4400
1.1670
0.9407
-27.403
29.362
-.516
-4619
27.615
34.446
8.506
4.774
Generation
= 0.25
SSIM
0,907
0.907
0.904
L.D 4
0.742
0.703
0.723
pMOS
3.095
3.060
3.073
== 1.0
SSIM
0.905
0.906
0,903
0.899
L.D 4
0.769
0.704
0.719
0.751
pMOS
3.082
3.044
3.063
2.976
Table 5: Reconstruction and generation performance under varying KI. divergence coefficients (VAE) and latent scaling factors (LBM). Reported on VCTK-test.
that std(2 8) 2 1, thereby constraining the amplitude range of the latent representation. This normalization consistently improves both objective and subjective metrics.
B.1.3 Comparison with baselines
Therefore, we set the compression rate to 512, reduce the KL-divergence to O, and apply latent scaling factor of s = 0.25, resulting in latent representation with frame rate of 100 Hz and 64 channels. After training for 1 million steps on the full dataset, we evaluate the reconstruction quality on the ESC-50 and VCTK-test sets and compare it against other baselines. As shown in Table 6 our model achieves the best reconstruction performance both in speech and audio domain across all metrics, which illustrates the advantage of using the compression network with relatively lower compression ratio and KL weight for AudioLBM.
B.2 Beyond 48 kHz compression networks
In our cascaded architecture, audio super-resolution above 48 kHz is achieved progressively across multiple stages. To avoid making the compression model (VAE) at higher sampling rates bottleneck, or introducing artifacts that compromise details reconstructed in earlier stages, we use unified compression ratio of 512 across all sampling rates.
However, high-resolution datasets (e.g., 96 kHz and 192 kHz) are relatively scarce. Training compression models directly on such data can significantly hurt generalization and lead to poorer reconstruction performance. Fortunately, consistent, a VAE trained at a lower sampling rate can be directly and effectively reused for higher sampling rates. Specifically, from the perspective as tine-compressed (i.c., faster-played) version of high-resolution audio, and thus still represents valid subset of the high-resolution distribution. Since low-resolution audio data (such 48 kHz) is more abundant, pretraining compression models on such data provides a strong and robust initialization, even in the presence of some distributional shift. As shown in Table 7 using compression model pretrained on 48 kHz already yields strong results on the 96Audio dataset. However, despite the much smaller dataset size, directly pretraining at kHz still achieves better performance under the test dataset with native 96 kHz distribution, suggesting domain gap between the two resolutions. Nevertheless, lightweight 200k-step fine-tuning on top of the 48 kHz-pretrained VAE surpasses both models, demonstrating strong transferability with only 20% training resource.
find that as long the compression ratio remains
96 kHz VAE, 48 kHz audio can be interpreted
30

---

fr
Model
SSIM 1
LSD +
LSD-LF +
LSD-HF 4
VCTK (48 klzz)
100 Hz
age
(continuous)
0.913
0.762
0.766
0.741
50 Hz
age
3
(discrete)
0.917
0.789
0.754
0.768
150 Hz
encodec 21
0.887
1.126
0.761
1.176
75 Hz
audiodec 115
0.922
0.939
0.944
0.937
Hz
flowdee
114
0.925
0.619
0.560
0.630
Ours
0.951
0.580
0.428
0.602
ESC-50 (44.1
kHz)
100 Hz
ago (continuous)
0.730
0.836
0.748
0.840
50 Hz
ago
3
(discrete)
0.741
0.852
0,703
0.862
Hz
encodec 21
0.704
0.925
0.910
0.922
100 Hz
dac 48
0.734
0.799
0.735
0.801
75 Hz
audiodec
115
0.695
0.999
0.969
0.997
75 Hz
flowdec
14
0.717
0.899
0.810
0.908
100
Ours
0.789
0.763
0.544
0.785
Table 6: Comparison of reconstruction quality across baselines on VCTK and ESC-50 test sets (resampled to 48 kHz and 44.1 kHz, respectively).
Step
Phase
Model
fr
SSIM LSD 4
LSD-LF + LSD-HF
96Audio dataset
100w
pretrain
48 kHz-vae
50Hz
0.815
0.808
0.815
0.774
100w
pretrain
96 kHz-vac
50Hz
0.818
0.798
0.803
0.772
100w
pretrain
48 kHz-vae
100Hz
0.840
0.811
0.821
0.760
100w
pretrain
96 kHz-vae
100Hz
0.841
0.731
0.747
0.698
20w
finetune
finetune from 48e
100Hz
0.850
0.709
0.703
0.692
192Audio dataset
100w
pretrain
192 kHz-vae
100Hz
0.868
0.736
0.643
0.752
100w
pretrain
96 kIlz-vae
100Hz
0.862
0.747
0.646
0.763
100w
pretrain
48 kHz-vae
100Hz
0.863
0.750
0.692
0.748
20w
finetune
finetune from 96 kHz- vae
100Hz
0.866
0.722
0.630
0.740
20w
finetune
finetune from 48 kHz-vae
100Hz
0.871
0.713
0.603
0.737
Table 7: VAE reconstruction results using different training strategies.
We observe similar trends in the 192Audio dataset: models fine-tuned from either 48 kHz or 96 kHz initialization outperform those trained from seratch 192 kHz. Interestingly, fine-tuning from 48 kHz-pretrained VAE consistently leads to better results compared to fine-tuning from 96 kHz- pretrained VAE, highlighting that the scale of pretraining data matters more than resolution proximity. In other words, pretraining on larger datasets at lower sampling rates yields more transferable and stable compression models for high-resolution audio.
C Foundation of bridge models
Bridge models provide a principled and efficient solution for inverse problems and conditional generation in settings where the prior is non- oon-Gassiian yet partially aligned with the target distribution.
Given sample from the prior distribution Tprior and its correspondence from target distribution Zarget In score-based generative models (SGMs) 198) forward SDE is defined between
Turget ~
Plarget and FT Fprior ~ Pprior:
dx; f(x,,t) t) dt g(t) dw:.
(9)
31

---

Here, t E [0, T] represents the current time step, with 2; denoting the state of data in the process, The drift is given by the vector field f. the diffusion by the scalar function g. W, the standard Wiener process, and the reference path measure ptf describes the probability of paths from Ppeior and Purget-
Under the above framework with boundary constraints, the Schrödinger bridge (SB) problem 94 14 seeks to find path measure p of specified boundary distributions that minimizes the Kullback-Leible divergence DKL. between a path measure and reference path measure Pref"
min (p || p
s.t. Pu
Ppriurs Pr Pdatas
(10)
pEP
where PI denotes the collection of all path measures over the time interval [0, T). In SB theory [08
14, this specific SB problem can be expressed as a pair of
linear SDEs:
dæ; [S (an, t) + (1) log Vr (1+) dt + g(t)dur,
(11)
dz; = f (z,, t) - ( log 1h (xx) dt + g(t)
(12)
where the non-linear drifts V log V (sre) and V Vlog (3:))
be described by coupled partial
differential equations (PDEs). A closed-form solution for SB [1] exists when Gaussian smoothing
is applied with Po W (IIR, T) and pr N (IIR, T..). the original Dirac distribution. By
( dr, and of =f' (²(r) dr, with boundary defining a elo f(r)dr 02 eli f(r)dr of fo at conditions and linear Gaussian assumption, tractable form of SB solved as
a²
1 = N (a12,a0o]]]
V = (ā.y,
(13)
under cr el f(r)ds Gaussian:
co and co +
14 Therefore, marginal distribution of xa at state is also
0 To
àoي? pT
0
Pc v V., N
(14)
of
of
D
Cascaded LBMs
In this section, we provide a detailed description of the cascaded LBM, including analyses of the proposed waveform-based and latent-based augmentation techniques.
D.1 Waveform-based filtering augmentation
Samples generated from the any-to-48 kHz stage often exhibit small-scale high-frequency artifacts, as shown in Figure (a). Directly feeding such artifacts into the next-stage super-resolution model can significantly degrade performance, as shown Figure (b) where high-frequency content becomes difficult to reconstruct. To address this, we apply Chebyshev Type-I low-pass filters (order=8) with sharp frequency roll-off in the spectral domain, as shown in Figure I0 (c)- removing a frequency content of 8 kHz, 4 kHz, and kHz, respectively, before feeding them into the next-stage model. The resulting outputs are shown in Figure 10 (f) (f).
As shown in Figures 10 (g) and (h), moderate filtering removes unwanted fighfrequency artifacts while preserving useful mid- fiddfrrquency information, enabling the model to generate nighfrreuency details more effectively. However, overly aggressive filtering, such as in Figure 10 (g). eliminates too much information. This forces the model to simultaneously reconstruct missing mid-to-low frequency content and synthesize high frequencies, resulting in over-smoothed outputs compared to the result in Figure (h).
The quantitative results presented in Table validate our findings. We conduct super-resolution experiments on both 48 kHz waveform generated by preceding 16-+48 kHz model (denoted as Generated) and 48 kHz audio obtained by downsampling real 96 kHz recordings (denoted as Real). For the Generated setting, waveform- -baed augmentation proves consistently effective across all filtering scales, with a moderate filtering ratio achieving the best trade-off between artifact removal and content preservation. Notably, for the Real setting, although inference benefits most from models trained without filtering, applying dynamic waveform-base based augmentation during training still leads to improved performance. This suggests that waveform-based augmentation remains beneficial in both synthetic and real-data scenarios, highlighting its general applicability and robustness.
32

---

generate
Small scale artifactss
high-frequency
16 to 48 KHz super-resclutin sample
w/o wav-based augmentation
(a)
Filtering scale argumentation
(b)
Large
Medium
Smell
(d)
(e)
(f)
(
Figure 10: Visual comparison of waveform- based filtering strategies. (a) shows the baseline output from the any-to-48 kHz stage with high-fre feeh-freeuency artifacts. (b) demonstrates that direct super- resolution from such inputs results in degraded high-frequency reconstruction. (c)-(e) apply low-pass filters with different cutoff frequencies, and the corresponding outputs after super-resolution are shown (f)-
999
SR on Generated kHz waveform
SR on
kHz waveform
Filter Ratio: 24-8
kHz
kHz
20
kHz
w.o.
12 kHz
kHz
kHz
21 kHz
w.o.
LSD 1
1.532
1.495
1,520
1,534
1,518
1.147
1.193
1.122
0.978
1.282
SSIM
0.539
0.541
0.539
0.538
0.537
0.763
0.762
0.766
0.767
0.757
Table 8: Ablation study waveform-based filtering augmentation for 48 +96 kHz super-resolution on the 96Music dataset.
D.2 Latent-based blurring augmentation
To improve the alignment between the predicted and ground-truth latents in the first stage. introduce blurring augmentation strategy applied to the latent of the upsampled waveform from previous stage. Specifically, after performing maveform-base Ierradation--harr small portion of high-freqeency spectral content is removed using low-pass filtering obtain a degraded latent representation HHR $
33

---

Specifically, we apply one-dimessional Gaussian blurring to each channel of zH which helps smooth local fluctuations and provides stable initial point for bridge sampling:
Sprior (t) Blur (zHR)
ZHR [c((t -), w(r) = w(T) z
Z exp 26
(15)
where c E [1, cz). b, denotes the blur ratio, is half the kernel size, and is the normalization constant ensuring -, w(r) = 1. We choose kernel size of 5, which is significantly larger than 36,, ensuring sufficient coverage of the Gaussian support. During training, the blur ratio b, is uniformly sampled from the range (0, 1).
High-frequency relative low-energy
Zoom-in compartson
Input
(8)
Intent-booee augmentation
Unclear harmonics
(8)
Blurring scale
Small
Medium
(0)
Figure 11: Visual comparison of latent-based based blurring strategies. (a) shows the baseline output from the any-to-48 kHz stage, where unclear harmonics and low high-frequency energy can be observed. (c)-(g) illustrate the effect of applying different blur ratios b,- = 0.05, 0.3, 0.5 to the prior latent during bridge sampling. (b) (d) show zoom-in views of (e)-g) respectively for closer inspection.
As shown in Figure I in addition to the small-scale high fregufrryeency artifacts described in Section D.I the generated samples may also exhibit unclear harmonics or relatively low energy in the high- frequency both of which negatively affect downstream stages and lead to cascading errors.
To address this, we apply different degrees of prior blurring with b, = 0.05, b, 0.3, and b, = 0.5. as shown in Figures (e) with zoom-in comparisons (b)-(d). The results demonstrate that latent-based augmentation effectively mitigates the imperfections in the input prior and improves overall reconstruction quality. not only enhances high-frequency generation but also improves low- frequency reconstruction, leading to more balanced spectral energy and clearer harmonic structures.
Among them, Figure (f) (with 6, 0.3) yields the best result. A smaller blur ratio, as in Figure [I (c). may not sufficiently correct low-frequency inconsistencies. while larger blur ratio, as in Figure (g), may overly smooth useful details, resulting in insufficient high-frequency generation. As shown in Table applying latent-based blurring significantly improves performance over the aa-aummentation baseline. moderate blur ratio (b, 0.3 for generated, b, - for real inputs) yields the best trade-off, effectively reducing high-frequency artifacts while preserving essential structure. From the results on SR on Real 48 kHz waveform, we observe a similar trend as discussed in Section D.I applying stronger blurring generally leads to worse performance on real data, as low-frequency content is already accurate and does not require correction. This suggests that during inference, only small or near-zero blur ratio is needed for real 48 kHz data. Nevertheless, applying
34

---

48 996 kHz SR
SR
Gemerated 48 kHz waveform
SR on Real 48 kHz waveform
Blur Ratio:
0.4
0.3
0.25
0.20
w.o.
0.35
0.25
0.15
0.05 w.o.
LSD SSIM 1
1.399
1.361
1.377
1,380
1.405
1.196
0.984
0.978
0.976
0.995
0,531
0.542
0.543
0.538
0.540
0.735
0.769
0.771
0.771
0.759
Table 9: Ablation study on latent-based blurring augmentation for 48 the 96Music dataset.
48-+96 kHz super-resolution on
mild level of blurring during training still outperforms the no-blur baseline (yielding a 0.02 reduction in LSD and a 0.01 improvement in SSIM), which may be because such operation promotes better understanding of low-frequency content, thereby enabling the model to generate high-frequency components more effectively.
E
Additional results
In this section, we first continue our discussion on the cascaded stage and present a comparison of several additional augmentation strategies and their effects. We then analyze the role of the low-frequency replacement technique, comparing its use in our system and in other baseline methods.
E.1 Other augmentation techniques
We additionally compare three alternative augmentation strategies: (1) latent noise, where Zprior
eHR + n, (N0, I); (2) pixel blur, where Tprioo = Blur( (llr((:HR) and (3) pixel noise, where Tiprior HR + NO, I).
latent
latent blur
pixel blur
latent noise
latent noise
latent noise
latent noise
pixel noise
Method
blur (fixed)
w/o
(dyn)
b,/
0.3
0.3
0.1
0.1
0.2
0.3
0.4
0.1
LSD 1
1.186
1.182
1,234
1.381
1.389
1.385
1.394
3.461
1,219
SSIM
0.733
0.738
0.731
0.728
0.728
0.725
0.725
0.397
0.734
Table 10: Ablation study comparing different prior augmentation strategies for bridge-based super-
resolution. The second row indicates the blur/noise ratio (b,/n,,) used in each method.
We observe that latent blurring consistently outperforms other strategies, especially when using dynamic blur ratios during training. Pixel-level noise introduces instability and fails to converge, while random latent noise degrades gradually with increased noise levels. This suggests that randomized augmentation may not be suitable for bridge models, while deterministic methods such as blurring offer more stable and reliable guidance. Compared pixel blurring, latent blurring provides more global and structured form of regularization, which better aligns the fow-frequency components with the ground-truth during training.
E.2 Low-frequency replacement
Low-frequency replacement is a widely adopted post-processing technique in super-resolution sys- tems, particularly in super-resolution models based on compressed representations [60] 62 122 37
Table IT presents the results of applying post-processing within our cascaded architecture. Specifi- cally, we apply low-frequency replacement the output of the any-to-48 kHz model by substituting the sub-1e 16 kHz frequency band with the corresponding band from the input waveform, resulting in the 48 kHz post variant. This serves the input for the subsequent 48 986 kHz super-resolution stage, producing 96 kHz post. Finally, a second round of fow-freqyy replacement is performed on the output waveform to yield the Final post result.
From the table, we observe that performing post-procsssing at the 48 kHz stage significantly improves low-frequency fidelity, as reflected by improvements in LSD (0-48 Hz: 2.714 - 2.437) and ViSQOL
35

---

Cascaded (w/o post)
48 kHz
48 kHz
96 kHz
Final
Band (Hz)
Metric
Direct
Upsampling
Post
Post
Post
0-48
LSD 4
3.785
1,552
2.714
2.437
1.314
1.291
0-16
LSD-LF +
0.186
0,485
0.811
0.331
0.522
0.342
16-48
LSD-HIF +
5.071
1.738
1.614
1.596
1.221
1.220
48-96
LSSDSFF 3.329
1.603
3.532
3.141
1.507
1.487
0-48
ViSQOL. 1.954
2.602
3.073
3.144
3.119
3.137
Table 1I: Ablation study of low-frequency replacement as a post-processing technique for 16 16-99 kHz super-resolution the 96Music dataset. Direct denotes any-to-96 kHz model; Cascaded (w/o post) denotes the raw output from cascaded LBMs without replacement; Post indicates low-frequency replacement at corresponding stages.
Method
Modeling Space
Method Type
RTF 4
NFE
Ours (any 48 kHz)
Wav-VAE
Bridge
0.369
Ours (any - 96 kHz)
Wav-VAE
Cascaded Bridges
0.695
100
Ours (any
192 kHz)
Wav-VAR
Cascaded Bridges
1.351
150
Bridge-SR 55 48 kHz
Waveform
Bridge
1.670
50
UDM+ 60 48 kHz
Waveform
Unconditional Diffusion
2.320
100
AudioSR 62 48 kHz
Mel-VAR VAE
Conditional Diffusion
0.948
50
Fre-painter [41] 48 kHz
Mel
GAN
0.009
1
NVSR (60) 48 kHz
Mel
GAN
0.033
1
Table 12: Real-time factor (RTF) results NVIDIA-A880 under the 48 kHz setting, as well as several baselines.
(3.073 3.144). More importantly, starting the 48-+9 kHz super-resolution from more accurate low-frequency foundation leads to better high-frequency generation, shown by the LSD-SF (48- 96 Hz) improvement from 1.603 1.507.
Although the 48 48696 kHz stage may slightly degrade the low-freyuency components again, we find that performing an additional round of low-frequency replacement the final 96 kHz waveform helps recover this degradation. As a result, we achieve a comparable overall fidelity in the 0-48 kHz band (ViSQOL: 3.137 vs. 3. 144), confirming the effectiveness of post-processing in both any-to-48 kHz and cascaded LBMs settings.
E.3 Inference computational cost
To comprehensively evaluate the efficiency, report the real-time factor (RTF) NVIDIA-A800 and several baselines under the 48 kHz setting in Table
It is worth noting that under the 48 kHz setting, although our method is not fast GAN-based approaches such as 600 41, due to the iterative sampling nature, significantly outperforms other iterative-basee based methods including (54) and the previous state-of-the-art system AudioSR (62]
When scaling to higher sampling rates (e.g., 192 kHz), naturally leads slower inference speeds. We mitigate this impact by adopting lighter network architecture (see Appendix G.2), so the inference speed does not increase linearly with the sampling rate. As shown in Table [2] even when upsampling to 192 kHz, our system is still faster than the 48 kHz waveform-domain bridge system (54).
E.4 Modeling space and other probabilistic methods
To isolate the contribution of the latent- latent-bridge formulation, we conducted additional experiments using the same speech datasets (OpenSLR (43, Expresso 755, EARS [86), and VCTK-Train (18) for training all models, and evaluated them on the VCTK-Test set. We compare the following variants without any additional modules, each trained with 500K steps on the any-to-48 kHz setting and tested on the 8-to-48 kHz SR setting with 50-step sampling:
36

---

Method
Modeling Space
SSIM
LSD
LSD-LF 4
LSD-HF
SigMOS [87
Diffusion
Mcl-VAE latent
0.809
0.940
0.486
0.994
2.846
Rectified Flow
Mel
0.784
0.816
0.194
0.889
2.792
Bridge
Complex STFT
0.809
1.295
0.414
1.401
2,951
Bridge
Raw waveform
0.660
1.037
0.184
1.101
2.896
Rectified Flow
Ours Wav-VAE latent
0.880
0.751
0.793
0.722
2.892
Diffusion
Ours Wav-VAE latent
0.879
0.758
0.806
0.728
2,741
Bridge (Ours)
Ours Wav VAE latent
0.907
0.742
0.708
0.712
3.095
Table I3: Comparison of different generative paradigms under the 8-to-48 kHz SR setting. All
models trained on the same datasets for 500K steps.
Latent Diffusion (on Wav-VAE latents)
Latent Rectified Flow (on Wav-VAE latents)
Bridge-STFT (based on the Nemo [33 framework)
Bridge-Waveform Waveform (based on Bridge-SR [54)
Latent Bridge (Ours)
As shown in Table 13 our latent-bridge model achieves higher SSIM, lower LSD (objective qual- ity), and better SigMOS (subjective quality), supporting that the latent-domain bridge formulation contributes significantly to the final performance, even when controlling for model architecture and training data.
F Inference techniques
In this section, we will discuss the low-pass filtering preprocessing method designed to handle real-world downsampled data.
F1 Filtering preprocessing for real-world data
Metric
Cheby1
Ellip
Bessel
Butter
LSD +
0.977
0.996
1.193
1.017
LSD-LF +
0.814
0.814
0.811
0.810
LSD-HF
0.989
1,011
1.236
1,036
SSIM t
0.693
0.690
0.664
0.686
Table 14: Comparison of different low-pass filters applied for super-resolution inference. Metrics are reported 16-+48 kHz super-resolution.
Even though we adopt various randomized low low-pass filters during training to simulate real-world low-resolution audio, we empirically find that it is beneficial to additionally apply low-pass filter to the upsampled low-resolution waveform during inference. In particular, the filter should ideally exhibit sharp roll-off in the frequency domain.
we compare four classical low-pass filters Chirrs-hhe Type I, Butterworth, Bessel, and Elliptic- for post-upsampling filtering, and evaluate their effeects on 16-+4 kHz super- resolution performance on the ESC-50 test set.
As shown in Table 14,
We observe that both the Chebyshev and Elliptic filters lead to better super-resolution results, as they feature faster attenuation in the stopband. contrast, Butterworth and Bessel filters exhibit slower roll-off. We hypothesize that this is because the model may struggle to distinguish whether the observed high-frequency attenuation originates from true characteristics of the data or from filtering artifacts introduced during preprocessing. In the former case, the model may mistakenly learn to continue the attenuation trend, which can impair its ability to effectively generate tighffreyuency components.
37

---

G Detailed experiment settings
G.1 Training dataset
Sampling Rate
Dataset
Duration
Type
VCTK-train
118
40h
Speech
OpenSLR
4
190h
Speech
EARS 86
100h
Speech
Expresso 75
20h
Speech
48 kHz
MusDB18
32
10h
Music
Medleydb
10h
Music
[InternalMusic]
2000h
Music
FSD50K 29
100h
Sound
[Interna/Sound]
2000h
Sound
[InternalMusic]
90h
Music
96 kHz
[Interna[Sound]
150h
Sound
[InternalMusic]
5h
Music
192 kHz
[InternalSound]
10h
Sound
Table 15: Overview of training datasets used at different sampling rates, including both public and internal sources.
To support multi-rate audio super-resolution, we curate diverse set of training datasets spanning speech, music, and sound domains across three sampling rates: 48 kHz, 96 kHz, and 192 kHz. As shown in Table [5] As shown in Table [5] We can also observe that high-resolution data becomes increasingly scarce as the sampling rate increases.
G.2 Model architecture
We adopt the Diffusion Transformer (DiT) architecture as the noise predictor for our bridge model, following the design of Stable Audio Open 288 During training, employ the Bridge-gnat gmax schedule, which has been proven effective in previous super-resolution and text-to-speech tasks [54] 14]. The network architecture and training configurations for the three-stage cascade are detailed below.
Any-to-48 kHz Stage
Model:
Depth: 24 layers
Attention heads: 24
Hidden dimension: 1152
Scaling factor: 0.25
Training sample length: 245760 samples 12s)
Training: Model:
Batch size: 128
Optimizer: Adam with 31 0.9, 93 0.99
Learning rate: 1 x 10-5
Weight decay: 0
Training sample rate range: 2 kHz to 32 kHz
Bridge g 1.0
Bridge - 0.001
38

---

48-to-96 kHz Stage and 96-to-192 kHz Stage
Model:
Depth: layers
Attention heads: 16
Hidden dimension: 1152
Scaling factor: 1.00
Training sample length: 245760 samples (5.12s for 96 kHz 2.56s for 192 kHz)
Training:
Batch size: 128
Optimizer: Adam with 31 0.9, _32 - 0.99
Learning rate: 1 x 10-5
Weight decay: 0
Training sample rate range for 48-to-96 kH2: 32 kHz to 96 kHz
Training sample rate range for 96-to-192 kHz: 64 kHz to 192 kHz
Bridge Imux = 1.0
Bridge Pmin = 0.001
G.3 Evaluation metrics
is widely used metric for evaluating the performance of audio super-resolution methods. Given a signal and its super-resolved counterpart 3, their Short-Time Time Fourier Transforms (STFT) computed S STFT(s) and $ (S), where both S, $ RFx,, with F' denoting the number of frequency bins and T the number of time frames. LSD is defined as:
Log-Spectral Distance (LSD) Log-Spectral Distance (LSD) 25
T
S(f,t)² S(
LSD(S,))
log
(16)
F
f=1
Here, t(f.t) and ((f,t) denote the spectral magnitude at frequency f and time é for the original and super-resolved signals, respectively. LSD penalizes spectral discrepancies, and lower values indicate better perceptual similarity in the frequency domain. To evaluate performance over specific frequency band [f1, fal, we define a band-limited version of LSD as:
1 fi
s(f.t) S(f
(S, T
log10
(17)
fe
Structural Similarity (SSIM) While LSD is a point-wise spectral metric, Structural Similarity (SSIM) [113] overcomes its limitations by incorporating structural and contextual information. Originally designed for perceptual image quality assessment, SSIM compares local statisties of luminance, contrast, and structure. the context audio, we apply SSIM on log- maggituue spectrograms to capture spectral texture fidelity.
The SSIM score between reference S and super-resolved S is computed as:
(2ps.Ms. + + Sx) + E2) S) SSIM
(18)
(m2 # + + + +o² + +
k=1
Here, S₁ and S2 denote the k-th local 7 x 7 block in the spectrograms, K is the total number of blocks, and 6 0.01, <2 = 0.02 are stability constants following VoiceFixer 24 Higher SSIM values imply better preservation of spectral structure.
39

---

Virtual Quality Objective Listener (ViSQOL) To assess perceptual speech quality in an objective manner, we adopt the Virtual Speech Quality Objective Listener (ViSQOL) (15), a signal-based estimator of Mean Opinion Score (MOS) using spectro-temporal similarity.
ViSQOL (in audio mode) assumes sampling rate of 48 kHz and outputs MOS-LQQ scores ranging from to 4.75, with higher scores indicating better perceptual quality. However, since ViSQOL is designed for speech and only supports certain sample rates (e.g.. 16 kHz), we additionally employ SigMOS 87 to evaluate speech quality for 48 kHz scenario.
G.4 Subjective experiment
For the subjective listening test, we evaluate super-resolution performance on generative model outputs from three representative systems: MaskGCT [II]) Au2 [63], and QA-MDT (33.
which represent modern speech generation at 24 kHz and music/sound generation at kHz, respec- tively.
For speech, we randomly select 10 samples from the LibriSpeech-test set 77 as both the reference audio and the text prompt for MaskGCT generation. For music and environmental audio, we sample 10 examples each from the MusicCaps I and AudioCaps 440 datasets. To further assess performance on real-world music, we additionally include 10 music segments from the Dong-Desrriber dataset [68]. All audio clips are truncated to 5.12 seconds. For each test case, we present three versions to listeners: the input audio (Generated), the ouiput from AudioSR, and the output from our system (AudioLBBM), yielding total of 40 groups 3 samples 120 audio clips for evaluation.
Participants were presented with 40 randomly ordered groups, each containing the three versions described above.They were instructed to rate each sample based on holistic evaluation of fidelity, clarity, and overall sound quality. Higher scores indicate better perceived quality.
We collected total of 2400 ratings from 20 participants with diverse backgrounds. We then compute the average ratings across three domains- Speech, Music, and Audio Effects as shown in Figure in the Introduction. The results show that super- repee-resolution consistently improves the perceptual quality of low-sample-rate audio, confirming the value of upsampling for generative models. Furthermore, our system outperforms AudioSR across all domains, demonstrating the superior audio quality enabled by our approach.
H Related works
H.1 Detailed introduction of audio super-resolution baselines
represents the first attempt at applying diffusion models to waveform- level audio super-resolution. It builds on the WaveNet [106] structure and adopts the DiffWave [44 training paradigm to learn mappings from fixed low-resolution audio to 48 kHz waveform. To support evaluation across various input resolutions, we follow the official implemeentatio and train separate models for 8 kHz, 12 kHz, 16 kHz, and 24 kHz inputs, each for 1.5 million steps.
Nu- Wave. Nu-Wave 149
Nu-Wave 2. Wave 2 49 extends Nu-Wave by incorporating two key innovations: Short- thort-Time Fourier Convolution (STFC) and Bandwidth Spectral Feature Transform (BSFT). These additions improve harmonic modeling and allow support for any-to-48 kHz super-resolution. The model also adopts a fast generation scheme using eight predefined non-uniform sampling steps. For fair comparison, we use the pre-trained model made available by the authors
UDM+. UDM+ 120 retains the DiffWave-base architecture but deviates from Nu- Wave in train-
ing strategy. It uses unconditional diffusion modeling and injects low-resolution signal guidance in- ference through a 50-step uniform sampling process with low-frequency component replacement (67] Additionally, Manifold Constraint Gradient (MCG) 17 is introduced to better balance low- and high-frequency consistency during generation.
httpp::/githubb..cmmmmmsmss////
stttp:://github.cco//mmaee wwwp:///aaauuaaauuuuuaua222
40

---

Bridge-SR. Bridge-SR [54] adapts the Nu-Wave 2 architecture but introduces a key conceptual shift: instead of sampling from standard Gaussian prior, the model initializes directly from the low-resolution input. This bridge formulation allows high-quality any-to-48 kHz SR. Furthermore, employs data normalization strategies and frequency-awer loss functions improve the final reconstruction quality.
mdetGAN. indtGANN [96] targets the instability issues of complex-valuee neural networks in the STFT domain by operating in the Modified Discrete Cosine Transform (MDCT) domain. Rather than relying on post-vocoders, mdetGAN uses adversarial learning to generate high-fidelity waveform with phase consistency. We evaluate the model using the authors' official checkpoints covering four different input resolutions.
NVSR. NVSR [60] is a neural vocoder-based speech SR system tailored to handle wide range of upsampling factors and phase reconstruction challenges. It is composed of three main modules: (1) mel-bandwidth extension network based ResUNet; (2) TFGAN-powered (TO5) neural vocoder; and (3) post- prosesrocessing module. We use the official model checkpoint available at for our comparisons.
is the first bandwidth extension system to model the high frequeer phase explicitly. It leverages GAN-based framework to jointly predict amplitude and phase spectra using dual-stream CNN, where the two branches interact to reconstruct full-band audio from narrowband speech. Although does not support arbitrary-resolution inputs, we evaluate the four fixed-resolution models provided by the author
AP-BWE AP-BWE 65
AudioSR. AudioSR 62 is a ceneral-purpont diffusion based super- auper-resolution model capable of handling speech, music, and general audio inputs. It performs super-resolution in the latent space conditioned on low-resolution inputs and uses a two-stage cascade consisting of -nel-tpectrogram VAE and vocoder- waveform reconstruction. Benefiting from strong zero-shot generalization, we evaluate the model using the official implementation 10
FrePainter. Fre-Painter 41 introduces a masked autoencoder (MAE)-based framework for audio super-resolution. It employs an upper-band masking strategy during fine-tuning to simulate low- resolution inputs by masking high-frequenyy components. Additionally, a mix-ratio masking approach is utilized to enhance robustness across various input sampling rates. The model is pre-trained on large-scale datasets learn robust speech representations and is fine-tuned jointly with neural vocoder for waveform reconstruction. We evaluate the model using the official implementation
FlowHigh. FLowHigh [122] proposes an audio super-resolution method based on flow matching, aiming to overcome the sampling inefficiency of traditional diffusion models. It adopts an inpainting- style framework similar AudioSR but constrains
modeling space Mel-spectrograms. lightweight two-layer Transformer [107] is used as the velocity predictor. To further improve sampling efficiency, FLowHigh introduces a data-dependent prior instead of a pure Gaussian initialization, allowing for faster flow-based sampling. We evaluate the model using the official implementation
H.2
Cascaded modeling
H.2.1
Audio domain
Audio waveform are continuous and high- high-dimensional 64] training a monolithic network to synthe- size full-band signals is notoriously unstable and tends to lose high-frequency detail [16]. Recent work therefore favors cascade architectures in which each stage handles a narrower bandwidth or simpler representation.
41

---

Text/semantic - audio cascades. Early systems such as Jukebox (23 map text prompt through three VQ- (Q-VAE tiers-semantic, acoustic and waveform-bett decoding, Moñsai [93] reduces this to two latent-diffusion steps. More recent models, including AudioLM,, MusicI and MusicFlow [9]]] 81, first generate semantic tokens, then refine them into acoustic tokens that vocoder converts to the final audio. InspireMusic [233 pairs a transformer LM with flow-based super-resolution
decoder for long-form, high-resolution music, while YuE [21]] uses an LLM-based lyric encoder followed by lightweight vocoder, forming a two-stage lyric-to-song pipeline.
Super-reson resoluteso cascades. On the SR side, models improve fidelity by letting each block focus on limited frequency band: progressive up-sampling GANs (PU-GAN) [[6], coarse-to- phase extensions such as MS-BWE [66], and multi-band diffusion that processes sub-bands in parallel [92]. The work most closely related to ours, Noise-to-Musii [66, cascades two diffusion models (3.2 kHz + 16 kHz) and uses waveform blurring plus stochastic low-pass resampling to perform cascading augmentation.
H.2.2 Vision domain
similar multi-stage processing trend is evident in the vision domain. Cascade-resolution training progressively feeds the same network with increasingly finer inputs as seen in models like PixArt- 2[2 and SANA(TI6] -nnabling a single model to scale seamlessly to generate high-resolution images.
Text-to-Image cascades. Modern text-to-image -mage generation pipelines often employ cascaded ar- chitectures, where separate diffusion autoregressive models operate sequentially at increasing spatial resolutions. Early examples include CDM (55 DALLEE [3), Imagen (90), and Relay- Diffusion [T04). More recent advances, such View 3 127]. Matryoshka Diffusion Model (II, and FMboost [95]. incorporate hybrid approaches combining diffusion models or flow models. Pipelines like SDXL (0) enhance the image quality of Stable Diffusion [88 through explicitly incorporating multi-resolution enhancement and refinement stages.
Super-resolution cascades. Super-resolution systems built on diffusion models also adopt cascaded frameworks. Methods such Inf-DiT [199] and SR3 [9]] perform iterative refinement, while Pixel- Space Laplacian Diffusion [2] leverage successive Laplacian pyramid- based enhancements. Together, these works confirm that allocating separate generators to coarse layout and fine detail is crucial for stable training, fast sampling, and high-fidelity ultra-resolution imagery.
I Qualitative results
In this section, we present two subsections of case studies. The first subsection compares the super-resolution performance of bridge models trained different representation spaces. The second focuses on therry-pickee samples from the demo page of A [45), which provides a strong baseline for comparison.
L1 Modeling on different audio spaces
In this section, compare three bridge models: (1) following Bridge-SR [54]. train 10.6M- parameter network based on a large WavNet [106] architecture on our dataset; (2) following NVIDIA- NeMo 46
construct bridge model directly the STFT spectrogram, treating each time frame as a token and modeling it with DiT (Diffusion Transformer (4) architecture of 0.3B, also trained
dataset; and (3) our proposed any-to-48 kHz AudioLBM system. As shown in Figure 12 waveform-based bridge models perform reasonably well on speech data but remain constrained by limited model capacity. When applied more diverse content such music and sound effects, these models fail to generalize, resulting in blurred high-frequency components and weak spectral energy. In contrast, STFT-based models can roughly capture the relationship between low and high frequencies; however, the high-frequenn details remain overly smooth, and harmonic structures are not well preserved-often leading to visible spectral discontinuities. Our proposed
42

---

Waveform
STFT
Wav-VAE latent
Ground Truth
Figure 12: Super-resolution results for bridge models on different modeling spaces.
AudioLBM demonstrates better generalization across all domains, yielding richer spectral detail and more consistent energy distribution across the frequency spectrum.
1.2 Comparison with cherry-picked samples non-cherry-picked results
In this section, we present qualitative comparison across five representative super-resolution baselines on the 8 kHz to 48 kHz task: AudioSR (62, ABBB [45). re-implemented 48 kHz version of Audit, CQTDiff [72 form from A SB [1] and our proposed method. As shown in Figure 13
Input
Ours
Input
Our
AudioSR
A2SB
AudioRR
A28B
Audit
COTDIT
Audir
CQTDAI
Figure 13: Qualitative comparison from A demo page.
approaches such as AudioSR and Audit, producing more complete, harmonic-rich, and structurally coherent high-frequency content. In contrast, direct data-space methods like A and CQTDiff tend to generate overly smooth outputs with blurred high-frequency regions and fail reconstruct clear harmonic cntters--especialyy visible in the blue box in the leftmost example.
our method clearly outperforms other
43

---

Input
AudioSR
Ours
Ground Truth
Figure 14: Additional comparison with AudioSR.
1.3 Additional Comparison
As shown in Figure 14 we further compare eight kHz to kHz super-resolution samples between our method and AudioSR. It can be observed that AudioSR, which performs spectral completion in the latent space, often produces excessively strong high-frequency components misalignments between high- and low-fre www-freueency regions. This suggests a limited ability to leverage the cow-frequency cues present in the input.
Additionally, due to the use multi-stage cascading compression network in AudioSR, fine spectral detail is often smoothed out, resulting in overly blurred outputs. In contrast, method aligns more closely with the ground truth and maintains strong coherence across the full frequency range. Moreover, thanks to the any-to-any training paradigm, system consistently generate full- bandwidth 48 kHz outputs, whereas AudioSR occasionally fails to fully reconstruct the high-frequency spectrum.
44


Reviews:
[{"review_id": "JxcYfvhmuW", "reviewer": "Reviewer_A2px", "summary": "This paper introduces AudioLBM, a novel audio super-resolution system based on latent bridge models. The core idea is to perform super-resolution as a latent-to-latent transformation. The work proposes frequency-aware training to enable \"any-to-any\" upsampling and a cascaded architecture with novel prior augmentation strategies to achieve state-of-the-art results and extend super-resolution to ultra-high sampling rates like 96kHz and 192kHz.", "questions": "1. The VAE's quality is fundamental to your method's performance. Could you please provide details on its architecture and its standalone reconstruction performance (e.g., SNR or LSD) to help us better understand the upper bound of your system?\n2. In the introduction, *\"As shown in Fig. 2, AudioSR [38] synthesizes the missing part of the mel-spectrogram latent representation from an uninformative Gaussian prior, ignoring the fact that the LR waveform contains informative cues about the HR target.\"* In contrast, Transformer or U-Net models can leverage the information in the LR waveform through self-attention and cross-scale feature aggregation mechanisms.\n3. In Section 3.1, *\"...rather than suffering from area removal in a latent space compressed by the STFT representation or mel-spectrogram [66].\"* Could you provide a more detailed explanation of what \"area removal\" means in the context of STFT?\n4. It is unclear why $z^{HR}$ and $z^{LR}$ have the same length $l$. Intuitively, the high-resolution waveform should yield a longer representation than the low-resolution counterpart for the same temporal duration. Could the authors clarify this?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strength\n1.   This paper propose an effective method for audio super-resolution at ultra-high sampling rates (up to 192 kHz), pushing the boundaries of audio SR and enabling professional applications such as audio mastering and post-production. \n2. The method demonstrates state-of-the-art performance across a wide range of audio types, including speech, music, and general audio. 3. The comprehensive experiments on multiple benchmark datasets (VCTK, ESC-50, SDS) show consistent and significant improvements over strong baselines in both objective (LSD, SSIM) and subjective (ViSQOL, SigMOS) metrics.\n\nWeakness\n1. The paper omits crucial details about the VAE autoencoder, such as its architecture and reconstruction performance, which is a core component and limits reproducibility.\n2. The motivation for using a bridge model is not well-justified against other method such as standard conditional diffusion model. \n3. The paper makes questionable claims about prior work, such as stating that AudioSR \"ignores\" informative cues or that spectrogram-based methods suffer from \"area removal,\" without sufficient explanation.\n4. Figure 2 does not clearly indicate which method corresponds to the proposed approach and which one represents AudioSR.", "was_revised": true, "final_justification": "Based on the authors' feedback in rebuttal, some of my concerns of the paper are addressed. So I raise the score.", "rebuttal": "We thank the reviewer for the valuable comments. We provide a point-to-point response as follows.\n\n### **Main Comments:**\n---\n#### **W1 and Q1: The VAE's quality**\n\nWe agree that the training and performance of the VAE are central to our method. Due to the limited space of the main paper, we have provided details on its architecture and its standalone reconstruction performance in **Appendix**.\n\nSpecifically, we examine the **reconstruction** performance and its corresponding **generation** performance by training our model for 200K steps **on each set of parameters**:\n\n- In **Appendix B.1**, we outline our VAE architecture and loss function, which closely follow the design and training pipeline of Stable-Audio-Open [1] and ETTA [2].\n- In **Appendix B.1.1**, we conduct a systematic exploration of compression rates tailored to the super-resolution task, ultimately choosing a 8× compression ratio, mapping the waveform $ \\mathbf{x} \\in \\mathbb{R}^L $ to $ \\mathbf{z} \\in \\mathbb{R}^{L/512 \\times 64} $.\n- In **Appendix B.1.2**, we further investigate the influence of the KL divergence weight, providing both quantitative results and qualitative insights.\n- In **Appendix B.1.3**, we include a detailed comparison of our VAE-based reconstructions with recent, open-sourced reconstruction baselines on 48kHz signals, as shown in **our four tables in the Appendix B**:\n\n\n| Frame Rate     | Model                | SSIM ↑ | LSD ↓ | LSD-LF ↓ | LSD-HF ↓ |\n|--------|----------------------|--------|--------|-----------|-----------|\n|        | **VCTK (48 kHz)**    |        |        |           |           |\n| 100 Hz | agc[3]  (continuous) | 0.913  | 0.762  | 0.766     | 0.741     |\n| 50 Hz  | agc[3]  (discrete)   | 0.917  | 0.789  | 0.754     | 0.768     |\n| 150 Hz | encodec[4]           | 0.887  | 1.126  | 0.761     | 1.176     |\n| 75 Hz  | audiodec[5]          | 0.922  | 0.939  | 0.944     | 0.937     |\n| 75 Hz  | flowdec[6]           | 0.925  | 0.619  | 0.560     | 0.630     |\n| 100 Hz | **Ours**             | **0.951** | **0.580** | **0.428** | **0.602** |\n\n| Frame Rate     | Model                | SSIM ↑ | LSD ↓ | LSD-LF ↓ | LSD-HF ↓ |\n|--------|----------------------|--------|--------|-----------|-----------|\n|        | **ESC-50 (44.1 kHz)**|        |        |           |           |\n| 100 Hz | agc  (continuous) | 0.730  | 0.836  | 0.748     | 0.840     |\n| 50 Hz  | agc  (discrete)   | 0.741  | 0.852  | 0.703     | 0.862     |\n| 150 Hz | encodec          | 0.704  | 0.925  | 0.910     | 0.922     |\n| 100 Hz | dac              | 0.734  | 0.799  | 0.735     | 0.801     |\n| 75 Hz  | audiodec         | 0.695  | 0.999  | 0.969     | 0.997     |\n| 75 Hz  | flowdec          | 0.717  | 0.899  | 0.810     | 0.908     |\n| 100 Hz | **Ours**             | **0.789** | **0.763** | **0.544** | **0.785** |\n- **Appendix B.2** covers the VAE training at higher resolutions (96kHz and 192kHz).\n\n---\n\n#### **W2 and Q2: Generation process and model architecture**\n\nWe would respectfully clarify that our discussion concerns the conceptual difference between **\"prior\"** and **\"condition\"** in the context of probabilistic generative processes, which respectively correspond to the **boundary distribution of generative process** and the **auxiliary indicative input of network network**.\n\nExploiting informative **prior distribution** with bridge models allows the sampling process to start from clean representations $\\mathbf{z}_ {T,\\text{bridge}}$ that are more instructive to the target than the noisy representations $\\mathbf{z}_{T,diff} \\sim \\mathcal{N}(0, \\mathbf{I})$ in conditional diffusion models, therefore reducing the burden of generation process and improving the generation results [7,8,9]. The **condition information** is provided as auxiliary model input, which can control both the noise-to-data generation direction of conditional diffusion models and the data-to-data direction of bridge models [10]. Hence, we respectfully clarify that, **prior** and **condition** are two different techniques for generative models, and improve the generation results from different perspectives. More details can be visited in following references: bridge models [7,8,9], and conditional diffusion models [10].\n\nIn audio super-resolution (i.e., **LR-to-HR**) task, as the LR observation has already provided instructive information for the HR target, we naturally improve previous **noise-to-data** generation process with the **data-to-data** one in bridge models, aligning our **boundary distributions** with the **LR-to-HR** task. Namely, both AudioSR and our AudioLBM contain condition information ,i.e., the LR obversation. Hence, the advantages of our method lie in **the constructed transition trajectory between LR and HR pairs**, which fully exploits the informative **LR prior**, rather than the external **condition** that encoded by specific model architecture.\n\nPreviously, in AudioSR, the prior $ \\mathbf{z}_ {T,diff} $ is drawn from a standard Gaussian distribution $\\mathcal{N}(0, I)$ which is not informative to the HR target. The diffusion trajectory is defined as:\n$\n\\mathbf{z}_ {t,diff} = \\alpha(t) \\cdot \\mathbf{z}_ 0 + \\beta(t) \\cdot \\boldsymbol{\\epsilon}, \\boldsymbol{\\epsilon} \\sim \\mathcal{N}(0, \\mathbf{I}),\n$\nwhere the sampling process starts from $\\mathbf{z}_ {T,diff} \\approx \\boldsymbol{\\epsilon}$ and **can not exploit instructive LR as prior for generative process**, forcing the model to reconstruct the full HR target purely via **sampling from noise**.\n\nIn contrast, our AudioLBM uses a bridge process, where the trajectory is explicitly defined between informative latent variables. Specifically, our formulation is:\n$\n\\mathbf{z}_ {t,bridge} = \\frac{\\alpha_ t \\bar{\\sigma}_ t^2}{\\sigma_ 1^2}  \\mathbf{z}_ 0+ \\frac{\\bar{\\alpha}_ t  \\sigma_ t^2}{\\sigma_ 1^2}  \\mathbf{z}_ {T,bridge} + \\frac{\\alpha_ t  \\bar{\\sigma}_ t  \\sigma_ t}{\\sigma_ 1}  \\boldsymbol{\\epsilon}, \\boldsymbol{\\epsilon} \\sim \\mathcal{N}(0, \\mathbf{I})\n$.\nHere, the intermediate latent representations $ \\mathbf{z}_ {t,bridge} $ has been a stochatisc interpolation between the HR latent $ \\mathbf{z}_ 0 $ and the LR latent $ \\mathbf{z}_ {T,bridge} $, which allows the generative process to **exploit the informative LR latent**.\n\nTherefore, despite the ability of architectures like Transformer or U-Net to extract and utilize low-frequency **condition**, their **generative process uses uninformative Gaussian prior**, which may lead to sub-optimal performance on audio super-resolution task. Namely, their sampling initiates denoising from Gaussian noise, resulting in a **noise-to-data** generation process whose **boundary distributions** are misaligned with the **LR-to-HR** up-sampling task.\n\nWe will clarify this with more explanations in the final version.\n\n---\n\n#### **W3 and Q3: Explanation of \"area removal\"**\n\nThank you for point that out. We would respectfully clarify that the term \"area removal\" is leveraged from recently proposed STFT-domain bridge model $A^2SB$ [11], refering to the phenomenon where high-frequency components are effectively filtered when using STFT or mel-spectrogram representations.\n\nTo elaborate, audio super-resolution aims to recover high-frequency components that are missing from low-resolution waveforms. In the frequency domain (e.g., STFT or mel-spectrogram), this typically manifests as blank or attenuated regions in the upper part of the spectrum, as illustrated in **Line 51** of our submission and reference **[12]**.\n\nWe will add more explanations to make this clearer in the final version.\n\n\n---\n\n#### **W4 and Q4: Explanation of Figure 2, $z^{HR}$ and $z^{LR}$**\n\nFigure 2 illustrates the training pipeline, in which the HR waveform is passed through a low-pass filter to simulate the LR signal. This filtering process preserves the *temporal duration* of the waveform, meaning that both HR and LR waveforms have the **same length** during training.\nTo clarify:  \n- The **top part** of Figure 2 illustrates how the **low-resolution waveform is simulated during training** using low-pass filtering.  \n- The **middle part** corresponds to the **baseline method AudioSR**, which synthesizes high-resolution target from uninformative Gaussian noise.  \n- The **bottom part** presents our proposed method, **AudioLBM**, which defines a bridge-based trajectories between informative LR and HR Wav-VAE latents.\n\nBefore inference, observed LR representation are typically shorter than the target HR represenatation in length due to lower sampling rate. To bridge this gap between inference and training, we **linearly upsample observed signal to the LR prior in the waveform space**, matching the target HR waveform length before compressing them into the latent space. This ensures temporal alignment and avoids train-test mismatch. This strategy is briefly mentioned in **Section 4.1** (\"Training Setup\"), and we will add more explanations to clarify this in the final version and make it more explicit in the experiment section to aid understanding of both the training and inference procedures.\n\n---\n[1] Stable Audio Open. ICASSP, 2025.\n\n[2] ETTA: Elucidating the Design Space of Text-to-Audio Models. ICML, 2025\n\n[3] AudiogenAI. AGC: Audio Generative Compression. Github Repo, 2024\n\n[4] High Fidelity Neural Audio Compression. TMLR, 2023.\n\n[5] Audiodec: An Open-source Streaming High-fidelity Neural Audio Codec. ICASSP, 2023\n\n[6] FlowDec: A Flow-based Full-band General Audio Codec with High Perceptual Quality. ICLR, 2025\n\n[7] Denoising Diffusion Bridge Models. ICLR, 2024\n\n[8] I2SB: image-to-image Schrödinger bridge. ICML, 2023\n\n[9] Schrödinger bridges beat diffusion models on text-to-speech synthesis. arXiv:2312.03491 (2023)\n\n[10] Why are conditional generative models better than unconditional ones?. NeurIPSW, 2022\n\n[11] A2SB: Audio-to-Audio Schrodinger Bridges. arXiv:2501.11311 (2025)\n\n[12] Time-frequency Networks for Audio Super-resolution. ICASSP, 2018\n\n---"}, {"review_id": "nXdv36v3eX", "reviewer": "Reviewer_sHec", "summary": "This paper presents a method to increase the bandwidth of an audio signal (\"super-resolution\") to a target frequency of sampling in an \"any-frequency-to-any\" fashion. The method operates by (conditioned) Shrödinger-Bridge diffusion over a latent-space representation obtained by a VAE on time-domain signals. An approach to cascade such models to reach higher frequencies that have no been considered in the literature before (96 kHz and 192 kHz) is also presented. A detailed experimental study including extensive comparisons to the state of the art on multiple datasets over objective and perceptual metric, and ablation study and a case study are presented.", "questions": "Questions and Suggestions:\n-  L11: \"the prior and target frequency\". Please specify: \"the prior and target *frequency of sampling*\" or *Nyquist frequency* or *max frequency* or *cut-off frequency* (otherwise not clear).\n- Please clarify in the caption of Fig. 2 what the 3 parts of the figure represent. If I understood right, the middle part is NOT the proposed approach but the competing approach AudioSR, while only the bottom part is AudioLBM (and I am not sure exactly if the top part represents one, or the two, or both, nor what it is meant to convey).\n- To justify upsampling to 96 kHz or above (which is not obviously useful a priori, at least to me), the authors first write \"allows flexibility in audio post-production\" at line 60 but provide no references, then \"provides further benefits\" at line 85 and cite [33,2,3,57] and then \"provides engineering advantages and post-processing flexibility\" and cite a different paper [51]. Please harmonize this by providing all of the relevant references every time.\n- L113: it would be good to specify here whether the VAE is trained on LR or on HR waveform (or both). I didn't find the information elsewhere in the paper.\n- L142: \"the diffusion-based audio upsampling\" -> what diffusion-based audio upsampling exactly?\n- L145: Could you please clarify what is meant by \"which has been aligned with\" here?\n- L155: \"while it has already provided\", I don't understand this sentence. What does \"it\" refer to here?\n- In the authors' framework, both HR and LR signals have the same length L. But it is not clear in practice how, given a shorter LR signal sampled at a lower rate, its size is increased to L. The authors only write at L231 \"all data are resampled to the corresponding target sampling rate\". But such process can be prone to artifacts that may impact the results. Please clarify how this was handled.\n- L164: please define the acronym DiT before and explain the corresponding model, for example here or when you introduce the training objective (2).\n- L166: why plural: \"bridge models\" ? are several models trained?\n- It would be nice to include some idea of the inference computational cost of the method (especially for the cascaded version, which the authors say is costly).\n- Typos\n    - L38, has->have\n    - L79: limited in specific domains -> to specific domains\n    - L170 - low-pass filtered\n    - L235 and L238: please improve/avoid the dual use of commas, eg (1,000,20,000), which makes it hard to read. (eg (1, 20) kHz instead)\n    - L291: \"sorely\" -> solely\n    - Beware of putting curled bracket around accronyms in bibtex references to make them appear correctly in the bibliography, e.g., Audiosr -> AudioSR", "limitations": "yes (end of conclusion).", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 4, "originality": 4, "strengths_and_weaknesses": "Strengths:\n- This is generally high-quality research, with a clear and reproducible presentation of the work. The reproducibility is strengthened by the addition of 24 pages of implementation details in appendix.\n- The topic is interesting and relevant\n- The intro and related work section are very well done and well written.The literature review is of high quality and thorough, with 70 citations.\n-  the new ideas of using latent bridge diffusion and of conditioning by the input and target frequencies are sound and well executed.\n- The techniques presented for cascading models are smart and original\n- The experiments are of high quality, including detailed comparison across many references, datasets and relevant metrics, an ablation study, and a qualitative case study.\n- The proposed approach clearly outperforms the state of the art over both objective and perceptual metrics across all test datasets.\n\nWeaknesses:\n- The motivation behind  upsampling audio signals to 96kHz or above is not clear. Features at that scales are clearly inaudible by the human auditory system. The authors mention \"allows flexibility in audio post-production\" -> is there some reference/evidence for this?\n- A few points should be clarified in the presentation of the method (see questions).", "was_revised": true, "final_justification": "I thank the authors for their clear and detailed responses. I stand by my recommendation of 5: Accept, which I think is well-calibrated for this submission.", "rebuttal": "We thank the reviewer for the valuable comments. We provide a point-to-point response as follows.\n\n### **Main Comments:**\n---\n\n#### **W1 and Q3: Motivation behind upsampling beyound 48 kHz and harmonize citation by providing all of the relevant references**\n\nWe will rigorously verify and manage citations regarding the role of ultra‑high sampling rate audio. Specifically, we will address our motivation in **mastering [1], post‑production [2,3], spatial audio[4], and immersive content creation[5]**. \n\nAs [1] shows, adopting 96 kHz permits gentler anti‑alias filters and greater headroom in the final master, albeit with higher data‑rate costs; [2] identifies near ultrasonic aliasing that intermodulates during editing and playback, advocating higher sample rates to suppress this distortion in production chains; [3] presents a meta‑analysis demonstrating a small but statistically significant perceptual advantage for high‑resolution audio under controlled listening conditions, supporting its use in critical post‑production monitoring; [4] provides psychophysical evidence that high‑frequency cues that are better preserved at ultra high sampling rates are vital for accurate spatial localization and [5] outlines coding strategies that maintain full‑bandwidth fidelity, a prerequisite for convincing, immersive playback formats.\n\n#### **Q1: Specify: \"the prior and target frequency of sampling\"**\n\nThe term \"frequency\" here refers to the **effective cut-off frequency**, as defined as $ \\text{SR}_ {x_ {\\text{HR}}} $ in Section 3.2 and explained as $ f_ {\\text{eff}} $ in Appendix A.1. This represents the **maximum frequency containing meaningful content** in the audio signal and is **independent of** the waveform’s sampling rate.\n\nIn our training setup, the LR signal is filtered from the HR waveform, sharing the same length. The prior and target frequencies we mention correspond to the **effective cut-off frequencies of the LR and HR waveforms**, respectively. These values are included as conditioning signals to enable the any-to-any super-resolution process described in Section 3.2.\n\nWe will add more explanations to clarify this in the final version.\n\n---\n\n#### **Q2: Clarify the caption of Fig. 2**\n\nThank you for pointing this out. To clarify:  \n\n- The **top part** of Figure 2 illustrates how the **low-resolution waveform is simulated during training** using low-pass filtering.  \n- The **middle part** corresponds to the **baseline method AudioSR**, which synthesizes high-resolution content from Gaussian noise.  \n- The **bottom part** presents our proposed method, **AudioLBM**, which defines a bridge-based trajectory between low- and high-resolution latent variables.\n\nWe will modify our caption of Figure 2 in the final version.\n\n---\n\n#### **Q4: Specify whether the VAE is trained on LR or on HR waveform (or both)**\n\nThank you for your valuable suggestion. Our 48 kHz VAE is trained **solely on the original 48 kHz (HR) resolution waveforms**,. We also experimented with supplementing the training data using low-pass-filtered (i.e., **LR**) versions of the same signals, but we did not observe improvements in reconstruction or super-resolution quality.\n\nTo address data scarcity at higher resolutions (96 kHz and 192 kHz), we adopt a staged training strategy, as described in **Appendix B.2**: we initialize the VAE with the weights from the lower sampling rate model and then **fine-tune** on the corresponding **HR** waveform data at each higher sampling rate. Please kindly visit our **Appendix B** for more details.\n\nWe will add more explanations on this point in the final version.\n\n---\n\n#### **Q5: L142: \"the diffusion-based audio upsampling\"**\n\nThe phrase \"diffusion-based audio upsampling\" refer specifically to the **AudioSR** baseline, which we use as a baseline throughout the paper illustrated in the middle part of Figure 2. We will add more explanations in the final version.\n\n---\n\n#### **Q6: L145: Clarify \"which has been aligned with\"**\n\nThank you for pointing this out. Here, \"which has been aligned with\" means that our boundary distributions, namely prior $z_ T^{LR}$ and target $z_ 0^{HR}$, have been aligned with the *LR-to-HR* task. We will make our expression more clarified in the final version.\n\n---\n\n#### **Q7: L155: \"while it has already provided\", I don't understand this sentence. What does \"it\" refer to here?**\n\nThank you for pointing this question out. As shown in our response to **Q1**, the term \"it\" here refers to the **effective cut-off frequency**, as defined in $ \\text{SR}_ {x_ {\\text{HR}}} $ in Section 3.2 and denoted as $ f_ {\\text{eff}} $ with explanation in Appendix A.1. We will make our expression here clearer in the final version.\n\n---\n\n#### **Q8: Length of HR and LR signals and potential upsampling artifacts**\n\nThank you for your valuable suggestion. The LR signals before inference are sampled at a lower rate and therefore have shorter lengths. Figure 2 illustrates the training process of our method, in which we simulate the upsampled low-resolution waveform by directly applying a low-pass filter to the high-resolution signal. In contrast, during inference, to ensure consistency in input-output alignment and support effective inference, we first upsample the LR waveform to the target resolution by **linear upsampling** before feeding it into the model as outlined in line 231.\n\nAs you noted, directly performing this step may introduce artifacts, however, our method **addresses** this with a **degradation-aware condition signal $ f_ {\\text{prior}} $** (see Section 3.2), which allows the model to **adaptively identify the effective frequency range of the input signal** and thereby mitigate the influence of such artifacts. We visualize this behavior in **Appendix A.2, Figure 4**, which shows how $ f_ {\\text{cond}} $ effectively help the model avoid artifacts during inference.\n\n---\n\n#### **Q9: L164: Define the acronym DiT**\n\nThank you for pointing this out. \"DiT\" stands for **Diffusion Transformer** [6] which serves as our score estimator. We will add it in the final version. \n\n---\n\n#### **Q10: L166: why plural: \"bridge models\"? are several models trained?**\n\nThe use of the plural form \"bridge models\" is intentional. In our framework, we adopt the latent scaling factor in each stage of our **cascaded bridge models** in Section 3.3, each responsible for performing super-resolution between three successive sampling rates. We use the plural form to indicate the cascading process.\n\n---\n\n#### **Q11: Inference computational cost**\n\nThank you for your valuable suggestion. Following your suggestion, we report the real-time factor (RTF) on an NVIDIA-A800 and several baselines under the 48kHz setting as follows:\n\n| Method                  | Modeling Space | Method Type              | RTF ↓  | NFE |\n|-------------------------|----------------|---------------------------|--------|-----|\n| **Ours (any → 48 kHz)**   | Wav-VAE        | Bridge                   | 0.369 | 50  |\n| **Ours (any → 96 kHz)**  | Wav-VAE        | Cascaded Bridges         | 0.695 | 100  |\n| **Ours (any → 192 kHz)**  | Wav-VAE        | Cascaded Bridges         | 1.351 | 150  |\n| Bridge-SR [7] 48 kHz          | Waveform       | Bridge                   | 1.670 | 50  |\n| UDM+ [8]  48 kHz              | Waveform       | Unconditional Diffusion  | 2.320 | 100 |\n| AudioSR [9]     48 kHz        | Mel-VAE        | Conditional Diffusion                | 0.948 | 50 |\n| Fre-painter [10]   48 kHz      | Mel            | GAN                      | 0.009 | 1 |\n| NVSR [11]  48 kHz              | Mel            | GAN                      | 0.033 | 1 |\n\nIt is worth noting that under the 48 kHz setting, although our method is not as fast as GAN-based approaches such as [10] and [11], because of the iterative sampling nature, it has significantly outperformed other iterative-based methods including [7], [8], and previous SoTA system AudioSR[9].\n\nWhen scaling to higher sampling rates (e.g., 192 kHz), it naturally leads to slower inference speeds. Especially, we mitigate the impact by adopting a lighter network architecture, as shown in *Appendix G.2*, so the inference speed does not increase linearly. As shown, even upsampling to 192 kHz, it is faster than the 48 kHz waveform-domain bridge system [7].\n\n\n---\n[1] Martin Link. Digital audio at 96 khz sampling frequency-pros and cons of a new audio technique. Audio Engineering Society, 1999\n\n[2] Richard Black. Anti-alias filters: the invisible distortion mechanism in digital audio? Audio Engineering Society, 1999.\n\n[3] Joshua D Reiss. A meta-analysis of high resolution audio perceptual evaluation. Journal of the Audio Engineering Society, 2016\n\n[4] Jens Blauert. Spatial hearing: the psychophysics of human sound localization. MIT press, 1997.\n\n[5] J Robert Stuart. Coding high quality digital audio. Japan Audio Society, 1997.\n\n[6] Scalable diffusion models with transformers. ICCV, 2023\n\n[7] Bridge-SR: Schrödinger bridge for efficient sr. ICASSP, 2025\n\n[8] Conditioning and sampling in variational diffusion models for speech super-resolution. ICASSP, 2023\n\n[9] AudioSR: Versatile audio super-resolution at scale. ICASSP, 2024\n\n[10] Audio super-resolution with robust speech representation learning of masked autoencoder. TASLP, 2024\n\n[11] Neural vocoder is all you need for speech super-resolution. Interspeech, 2022\n\n---"}, {"review_id": "zUvffvSFth", "reviewer": "Reviewer_UGNU", "summary": "This paper tackles the long-standing problem of sub-optimal audio super-resolution caused by uninformative generative priors. The authors propose an Audio Latent-Bridge Model (Audio-LBM) that first compresses a waveform into a continuous latent space and then learns a generative bridge from low-resolution (LR) to high-resolution (HR) latents. To reduce data scarcity at high sampling rates, they introduce a frequency-aware LBM that conditions on both LR and HR cutoff frequencies, enabling any-to-any up-sampling within a single model. A cascaded LBM configuration is further adopted to reach 48 kHz -> 192 kHz. To limit error accumulation across stages, two prior-augmentation techniques are applied: (i) waveform-domain degradation that removes fine-grained details near the Nyquist boundary, and ((ii) latent-domain dynamic Gaussian smoothing. Comprehensive experiments on speech, general audio, and music benchmarks show state-of-the-art results for any-to-48 kHz and, for the first time, strong baselines for any-to-192 kHz.", "questions": "- The paper states: “We directly compress the audio waveform into a continuous latent representation, where the latent of the LR waveform provides instructive information for the HR latent and avoids the discarded regions in previous works [20, 22].”\nCould you supply concrete evidence for this claim? There are many ways to map a waveform into a continuous latent space, and it is not obvious that the chosen compression actually preserves the information needed to reconstruct HR audio. Any experiments comparing alternative latent encoders (e.g., raw-waveform or mel-spectrogram latents) would help substantiate the point.\n\n- You argue that conditioning on both input and target cutoff frequencies allows the model to learn an any-to-any up-sampling process and boosts 48 kHz performance. The ablations indeed show a gain, but why does training with lower-band samples help when the final target is fixed at 48 kHz? A deeper analysis—attention visualizations, latent interpolations, or other diagnostics—would clarify the mechanism. Right now the paper attributes the gain mainly to larger data scale, which feels insufficient.\n\n- The ablation study covers dataset filtering and frequency awareness, but it does not isolate the benefit of the latent-bridge formulation itself. To make the argument stronger, please add direct comparisons with (i) latent diffusion models trained on the same latents and (ii) bridge models that operate on raw waveform or spectral representations. Such head-to-head results would clarify how much improvement truly comes from adopting a latent bridge versus alternative generative priors.", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\nThe paper presents a robust model that delivers consistently strong results for any-to-48 kHz audio super-resolution across speech, music, and general audio, clearly outperforming prior work. It backs this claim with extensive experiments and ablation studies that reveal how each proposed component contributes to the final quality. The released audio samples sound noticeably better than baselines, and the framework is scaled to 96 kHz and 192 kHz—rates that matter in industry yet are rarely explored in academia. Importantly, the authors do more than stack models: they introduce cascade-error-mitigation techniques that meaningfully curb quality degradation between stages.\n\nWeaknesses:\nWhile the system works well, the paper offers little scientific insight into why the latent-bridge approach yields more informative priors than diffusion or GAN alternatives. Discussion of broader applicability is limited to a brief “future work” remark, leaving unanswered how the method might generalize to other restoration tasks or modalities. A deeper analysis of the underlying mechanisms—and clearer guidance on extending the technique—would strengthen the contribution.", "was_revised": true, "final_justification": "I have thoroughly read the authors’ reviews and rebuttal, and many of my concerns have been addressed. While this paper is technically solid, I believe there are additional aspects that need to be addressed for its academic contribution to be applied to a broader domain, so I intend to keep my score unchanged.", "rebuttal": "We thank the reviewer for the valuable comments. We provide a point-to-point response as follows.\n\n### **Main Comments:**\n---\n\n#### **W1: little scientific insight into why the latent-bridge approach yields more informative priors than diffusion or GAN alternatives**\nThank you for pointing this out. We respectfully clarify the scientific motivation behind using the latent-bridge approach, which fundamentally lies in how it redefines the **prior distribution** of the generative process in a way that is more SR task-aligned and informative than the standard Gaussian prior used in conventional diffusion models.\n\nIn  diffusion models, the trajectory is defined as $\n\\mathbf{z}_ {t,diff} = \\alpha(t) \\cdot \\mathbf{z}_ 0 + \\beta(t) \\cdot \\boldsymbol{\\epsilon}, \\boldsymbol{\\epsilon} \\sim \\mathcal{N}(0, \\mathbf{I}),\n$ although the LR input is injected as a condition, the generative process itself starts from an uninformative noise prior (typically $\\mathbf{z}_T \\sim \\mathcal{N}(0, \\mathbf{I})$). This **noise-to-data** generation imposes a heavy burden on the model: it must learn to reconstruct the HR target solely from random noise, while separately relying on the condition for guidance. As a result, the **prior distribution is misaligned with the actual LR-to-HR task**, leading to inefficiency and potential degradation in performance.\n\nIn contrast, our latent-bridge model formulate:\n$\n\\mathbf{z}_ {t,bridge} = \\frac{\\alpha_ t  \\bar{\\sigma}_ t^2}{\\sigma_ 1^2} \\, \\mathbf{z}_ 0+ \\frac{\\bar{\\alpha}_ t \\, \\sigma_ t^2}{\\sigma_ 1^2}  \\mathbf{z}_ {T,bridge} + \\frac{\\alpha_ t  \\bar{\\sigma}_ t  \\sigma_ t}{\\sigma_ 1} \\\\boldsymbol{\\epsilon}, \\boldsymbol{\\epsilon} \\sim \\mathcal{N}(0, \\mathbf{I})\n$ and introduces a **data-informed** prior, where the sampling process starts from an LR latent representation that is already informative about the HR target. This establishes a data-to-data generation trajectory.\n\nMoreover, compared to GANs, diffusion and bridge models adopt **iterative sampling**, which enables the model to better capture fine-grained details, potentially leading to improved super-resolution quality.\n\n#### **W2: How the method might generalize to other restoration tasks or modalities**\n\nYour question is sincerely appreciated. We totally agree that more discussion of the underlying mechanisms can strengthen our contribution. Also, we provide our insights for extending this method to other restoration tasks as follows.\n\n**More discussion for generalizable training**: from our perspective, bridge models are advantageous in the tasks where the condition information is instructive to the generation target. However, without a compression network, directly designing a bridge model in the waveform space or the STFT representations may increase the burden of generative models, as the redundant information in the data space has to be accurately modelled with a single generative model.\n\nIn our method, we transform the **data-to-data** generation process into a **latent-to-latent** one with a waveform compression network, which preserves the advantages of bridge models on exploiting informative prior while enabling more compact and generalizable training, allowing our AudioLBM to improve the quality across speech, audio, and music samples as shown in the subjective quality results in our **Figure 1**.\n\n**Extending to other restoration tasks**: we think our method will be indicative to the design of bridge models on speech restoration tasks, especially the general speech restoration systems, as these tasks also require generalizable training and has indicative observation for the generation target. However, developing bridge models for these tasks should further consider their task-specific evaluation metrics, and then propose the innovative techniques suitable for these tasks.\n\n#### **Q1: The paper states: “We directly compress the audio waveform into a continuous latent representation, where the latent of the LR waveform provides instructive information for the HR latent and avoids the discarded regions in previous works [20, 22].” Could you supply concrete evidence for this claim? There are many ways to map a waveform into a continuous latent space, and it is not obvious that the chosen compression actually preserves the information needed to reconstruct HR audio. Any experiments comparing alternative latent encoders (e.g., raw-waveform or mel-spectrogram latents) would help substantiate the point.**\n\nThank you for your valuable suggestion. We agree that the connection between compression strategy and the preservation of HR information should be better articulated. \n\nHowever, we would like to respectfully clarify that the term \"discarded regions\", also referred to as \"area removal\", is **borrowed from** the recently proposed STFT-domain bridge model $A^2SB$ [1]. It describes the phenomenon in which high-frequency components are **effectively discarded** when using STFT or mel-spectrogram representations[2]. As the input has a lower effective frequency band, the area removal problem becomes more pronounced, making the inpainting task **increasingly challenging**.\n\nWe would also respectfully clarify that our discussion concerns the conceptual difference between **\"prior\"** and **\"condition\"** in the context of probabilistic generative processes, which respectively correspond to the **boundary distribution of generative process** (also the advantage of our bridge model compared to diffusion model) and the **auxiliary indicative input of network network**.\n\nTo substantiate our choice, we conduct additional experiments **(see Q3)** comparing waveform-based latent compression with alternatives using STFT and mel-spectrogram representations. These results confirm that our waveform latent preserves richer frequency content and leads to superior super-resolution performance.\n\nWe will make these motivations and comparisons clearer in the final version. Thank you again for helping us improve the clarity of our work, we will clarify this with more explanations in the final version.\n\n\n---\n\n#### **Q2: Deeper analysis of the *any-to-any* process**\n\nWe would like to clarify that, by defining these two conditions, our bridge models can gain a clearer understanding of the frequency boundary between the LR prior and the HR target in the bridge upsampling process. In other words, the generative process is explicitly conditioned on these two additional pieces of start and end points, enabling the model to jointly learn multiple super-resolution tasks during training. Hence, this finer-grained guidance allows the model to make more effective use of all available data (rather than relying solely on full-band inputs), and can generate desired full-band result even trained with waveforms suffered from limited effective frequency ranges, ultimately improving super-resolution performance.\n\n---\n\n#### **Q3: Add direct comparisons with (i) latent diffusion models trained on the same latents and (ii) bridge models that operate on raw waveform or spectral representations. Such head-to-head results would clarify how much improvement truly comes from adopting a latent bridge versus alternative generative priors.**\n\nThank you for the valuable suggestion. We agree that isolating the contribution of the latent-bridge formulation is important for a fair evaluation.\n\nTo address this, we have conducted additional experiments using the same speech datasets (OpenSLR [3], Expresso [4], EARS Dataset [5], and VCTK-Train [6]) for training all models, and evaluated them on the same VCTK-Test set.\n\nWe compare the following variants without any additional modules, each model is trained with 500K steps on the any-to-48 kHz setting and tested on 8-to-48 kHz SR setting with 50-step sampling:\n\n- Latent Diffusion (on wav-vae latents)  \n- Latent Rectified Flow (on wav-vae latents)  \n- Bridge-STFT (Based on the Nemo[5] framework)\n- Bridge-Waveform (Based on Bridge-SR[6]) \n- Latent Bridge (Ours)\n\n| Method                   | Modeling Space   | SSIM ↑ | LSD ↓| LSD-LF ↓| LSD-HF ↓|SigMOS[9] ↑|\n|--------------------------|----------------|--------|-------|-------|-------|------|\n| Diffusion[7] | Mel-vae latent| 0.809 | 0.940 |0.486|0.994|2.846 |\n| Rectified Flow[8] | Mel | 0.784 | 0.816 |0.194|0.889|2.792 |\n| ***Bridge***         | Complex STFT           |  0.809  | 1.295 | 0.414|1.401 |2.951|\n| ***Bridge***        | Raw waveform       |  0.660  | 1.037 |**0.184**|1.101| 2.896 |\n| Rectified Flow    | ***Ours wav-vae latent***     |  0.880    | 0.751 | 0.793|0.722| 2.892|\n| Diffusion         | ***Ours wav-vae latent***     |   0.879   | 0.758 | 0.806|0.728 |2.741 |\n| ***Bridge (Ours)*** | ***Ours wav-vae latent*** | **0.907** |  **0.742** | 0.708 | **0.712** | **3.095** |\n\nAs shown above, our latent-bridge model achieves both higher SSIM, LSD (objective quality) and SigMOS (subjective quality) score, supporting that the **latent-domain bridge formulation contributes significantly** to final performance, even when controlling for model architecture and training data. \nWe also provide some corresponding **visualizations** in **Appendix I.1** to make this clearer.\n\n---\n\n[1] A2SB: Audio-to-Audio Schrodinger Bridges. arXiv preprint arXiv:2501.11311 (2025).\n\n[2] Time-frequency Networks for Audio Super-resolution. ICASSP, 2018\n\n[3] Crowd-Sourced Speech Corpora for Javanese, Sundanese, Sinhala, Nepali, and Bangladeshi Bengali. SLTU, 2018.\n\n[4] Expresso: A benchmark and analysis of discrete expressive speech resynthesis. Interspeech, 2023\n\n[5] Speech enhancement and dereverberation with diffusion-based generative models. TASLP, 2023\n\n[6] Expressive neural voice cloning. ACML, 2021.\n\n[7] AudioSR: Versatile audio super-resolution at scale. ICASSP, 2024\n\n[8] Flowhigh: Towards efficient and high-quality audio super-resolution with single-step flow matching. ICASSP, 2025\n\n[9] ICASSP 2024 speech signal improvement challenge. IEEE Open Journal of Signal Processing, 2025\n\n---"}, {"review_id": "MFQjKhSETf", "reviewer": "Reviewer_X2LP", "summary": "The paper proposes to tackle audio super resolution using Latent Bridge Models (LBMs).\nThe authors propose to condition the LBM (bridging between low resolution input to high resolution output) on the input and target frame rates, therefore enabling any-to-any upsampling.\nThey also propose a super resolution model for very high sampling rates (up to 192kHz) using cascading LBMs and propose methods to mitigate the errors arising with multi-stage generation.\nThere's an accompanying website in which they compare their approach with AudioSR, a similar approach based on conditional Latent Diffusion Models.", "questions": "- Will the the models & code will be publicly available and reproducible?", "limitations": "Ideas in this paper are fairly standard so the main value of this work is in the models and their implication in the audio community.", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 4, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- Consider very high sampling rates (up to 192kHz) which is quite rare in the domain\n- state-of-the art performances. Clear improvements over audioSR. Examples on the accompanying website corroborate the good results on the metrics.\n- The modeling choices, if quite standard, are well-motivated (choice of LBM instead of LDM), conditioning on framerate to leverage more data, augmentations when cascading; which leads to a convincing ablation study.\n- Well-written and extensive comparison\n- Good justification about why 192kHz is sometimes required for professional use\n- If the model is released, this is an excellent contribution that may be quite impactful, as the community working on audio generative modeling could work at lower sampling rates without sacrificing audio quality.\n\nWeaknesses:\n- not clear if the models & code will be publicly available.\n- Lacking details on the high-res VAE.\n- Maybe the sampling time can be stated explicitly so that practitioners may assess if this methods", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for the valuable and inspiring comments. \n\n### **Main Comments:**\n---\n\n#### **W1 and Q1: If models & code will be publicly available**\nWe appreciate the reviewer's emphasis on reproducibility, which we also consider highly important. We will make our best efforts to release more implementation details and resources to support further research in the audio community, e.g., opening the inference implementation in the first step.\n\n#### **W2: Lacking details on the high-res VAE**\nWe agree that the high-resolution VAE plays a crucial role in our framework.\n\nIn fact, we have provided extensive details in **Appendix**, and we evaluate both the **reconstruction** and corresponding **generation** performance of our VAE by training for **200K steps** on each configuration. We train each ablated VAE configuration on our full speech corpus (details in **Appendix G**) for 200K steps, and pair it with a corresponding Latent Bridge Model (LBM) trained for 150K steps. All evaluations are conducted on the VCTK-test set. We kindly refer the reviewer to the following sections for more specifics:\n\n- In **Appendix B.1**, we outline the VAE architecture and loss formulation, which closely follow the training structure of **Stable-Audio-Open [1]** and **ETTA [2]**. Specifically, we adopt a Oobleck[3]-based compression network with DAC[4]-based discriminator.\n- In **Appendix B.1.1**, we conduct a systematic study of **compression ratios** for super-resolution, ultimately selecting a **512× compression** from waveform $ \\mathbf{x} \\in \\mathbb{R}^L $ to latent $ \\mathbf{z} \\in \\mathbb{R}^{L/512 \\times 64} $, and we find that a time-axis compression rate of 512 achieves the best trade-off between efficiency and performance.\n- **Appendix B.1.2** investigates the effect of **KL divergence weight**, and includes both quantitative analysis and interpretability discussion. We apply a fixed scaling factor s introduced in Section 3.2, line 166 as 0.25 and KL divergence as 0 (where our VAE degrades into an AutoEncoder).\n- **Appendix B.1.3** compares our VAE reconstruction quality against recent open-source baselines on 48 kHz audio.\n- **Appendix B.2** details the **training procedures for high-resolution VAE models** at 96 kHz and 192 kHz, including parameter choices and convergence behavior.\n\n##### 96Audio dataset\n\n| Step | Phase    | Model                      | frame rate    | SSIM ↑ | LSD ↓  | LSD-LF ↓ | LSD-HF ↓ |\n|------|----------|----------------------------|-------|--------|--------|-----------|-----------|\n| 100w | pretrain | 48 kHz-vae                 | 50Hz  | 0.815  | 0.808  | 0.815     | 0.774     |\n| 100w | pretrain | 96 kHz-vae                 | 50Hz  | 0.818  | 0.798  | 0.803     | 0.772     |\n| 100w | pretrain | 48 kHz-vae                 | 100Hz | 0.840  | 0.811  | 0.821     | 0.760     |\n| 100w | pretrain | 96 kHz-vae                 | 100Hz | 0.841  | 0.731  | 0.747     | 0.698     |\n| 20w  | finetune | finetune from 48 kHz-vae    | 100Hz | **0.850**  | **0.709**  | **0.703**     | **0.692**     |\n\n\n##### 192Audio dataset\n\n| Step | Phase    | Model                      | frame rate    | SSIM ↑ | LSD ↓  | LSD-LF ↓ | LSD-HF ↓ |\n|------|----------|----------------------------|-------|--------|--------|-----------|-----------|\n| 100w | pretrain | 192 kHz-vae                | 100Hz | 0.868  | 0.736  | 0.643     | 0.752     |\n| 100w | pretrain | 96 kHz-vae                 | 100Hz | 0.862  | 0.747  | 0.646     | 0.763     |\n| 100w | pretrain | 48 kHz-vae                 | 100Hz | 0.863  | 0.750  | 0.692     | 0.748     |\n| 20w  | finetune | finetune from 96 kHz-vae   | 100Hz | 0.866  | 0.722  | 0.630     | 0.740     |\n| 20w  | finetune | finetune from 48 kHz-vae   | 100Hz | **0.871**  | **0.713**  | **0.603**     | **0.737**     |\n\nFor the 96 kHz and 192 kHz VAEs, as shown in **Appendix B.2**, we adopt the same network architecture and training procedure as the 48 kHz VAE. Moreover, the higher-resolution VAEs are fine-tuned from the lower-resolution ones to alleviate the scarcity of ultra high-resolution training data. \nWe will make this clearer in the final version.\n\n---\n\n#### **W3: Sampling time can be stated explicitly**\n\nThe inference efficiency is indeed a key factor for the deployment of high-resolution audio generation models.\n\nTo address this, we present below the real-time factor (RTF) and number of function evaluations (NFE) of our method and several representative baselines on a single NVIDIA-A800, all evaluated under the 48 kHz setting:\n\n| Method                   | Modeling Space | Model             | RTF ↓ | NFE |\n| ------------------------ | -------------- | ----------------------- | ----- | --- |\n| **Ours (any → 48 kHz)**   | Wav-VAE        | Bridge                  | 0.369 | 50  |\n| **Ours (any → 96 kHz)**  | Wav-VAE        | Cascaded Bridges        | 0.695 | 100 |\n| **Ours (any → 192 kHz)**  | Wav-VAE        | Cascaded Bridges        | 1.351 | 150 |\n| Bridge-SR [5] 48 kHz     | Waveform       | Bridge                  | 1.670 | 50  |\n| UDM+ [6]  48 kHz         | Waveform       | Unconditional Diffusion | 2.320 | 100 |\n| AudioSR [7]     48 kHz   | Mel-VAE        | Conditional Diffusion    | 0.948 | 50  |\n| Fre-painter [8]   48 kHz | Mel            | GAN                     | 0.009 | 1   |\n| NVSR [9]  48 kHz         | Mel            | GAN                     | 0.033 | 1   |\n\nWhile our method may not match the inference speed of GAN-based models like [8] and [9], it offers a substantial speedup over other **iterative-based** models, including Bridge-SR [5], UDM+ [6], and previous SoTA AudioSR [7] (RTF 0.369 vs. 0.948).\n\nWhen scaling the sampling target to higher sampling rates (e.g., 192 kHz), it naturally leads to slower inference speeds beacuse of the cascade paradigm. Especially, we mitigate the impact by adopting a lighter network architecture, as shown in Appendix G.2, so the inference speed does not increase linearly. As shown, even upsampling to 192 kHz, it is even faster than the 48 kHz waveform-domain bridge system [5] (RTF 1.351 vs. 1.670).\n\nWe hope our reply can address your concerns!\n\n---\n\n[1] Stable Audio Open. ICASSP, 2025\n\n[2] ETTA: Elucidating the Design Space of Text-to-Audio Models. ICML, 2025\n\n[3] Long-form music generation with latent diffusion. ISMIR, 2024\n\n[4] High-fidelity audio compression with improved rvqgan. NeurIPS, 2023\n\n[5] Bridge-SR: Schrödinger bridge for efficient sr. ICASSP, 2025\n\n[6] Conditioning and sampling in variational diffusion models for speech super-resolution. ICASSP, 2023\n\n[7] AudioSR: Versatile audio super-resolution at scale. ICASSP, 2024\n\n[8] Audio super-resolution with robust speech representation learning of masked autoencoder. TASLP, 2024\n\n[9] Neural vocoder is all you need for speech super-resolution. Interspeech, 2022"}]

Author rebuttal:

Meta-review: This paper proposes a method for audio bandwidth extension (“super-resolution”) that supports arbitrary input–output sampling rates. The approach employs conditioned Bridge diffusion in a VAE-derived latent space, and further introduces model cascading to enable reconstruction at ultrahigh frequencies (96 kHz and 192 kHz).

Reviewers found the approach both novel and effective, with performance exceeding state-of-the-art baselines. During the rebuttal, the authors provided additional results and clarifications that successfully addressed all reviewer concerns. I highly encourage the authors to in corporate these into the final manuscript, it would further strengthen this work.

For the above reasons, I recommend acceptance of this submission.
Decision: Accept (poster)