BADiff: Bandwidth Adaptive Diffusion Model
Authors: Xi Zhang
Hanwei Zhu
Yan Zhong
Jiamang Wang
Weisi Lin
Venue: NeurIPS 2025 poster ()
Keywords: Bandwidth-aware generation
diffusion models
image compression
Primary area: deep_learning
TL;DR: We propose BADiff, a bandwidth-adaptive diffusion model that conditions image generation on a target entropy value to directly control perceptual quality under transmission constraints.

Abstract: In this work, we propose a novel framework to enable diffusion models to adapt their generation quality based on real-time network bandwidth constraints. Traditional diffusion models produce high-fidelity images by performing a fixed number of denoising steps, regardless of downstream transmission limitations. However, in practical cloud-to-device scenarios, limited bandwidth often necessitates heavy compression, leading to loss of fine textures and wasted computation. To address this, we introduce a joint end-to-end training strategy where the diffusion model is conditioned on a target quality level derived from the available bandwidth. During training, the model learns to adaptively modulate the denoising process, enabling early-stop sampling that maintains perceptual quality appropriate to the target transmission condition. Our method requires minimal architectural changes and leverages a lightweight quality embedding to guide the denoising trajectory. Experimental results demonstrate that our approach significantly improves the visual fidelity of bandwidth-adapted generations compared to naive early-stopping, offering a promising solution for efficient image delivery in bandwidth-constrained environments. Code is available at: https://github.com/xzhang9308/BADiff.

BADiff: Bandwidth Adaptive Diffusion Model
Xi Zhang' Hanwei Zhu E Yan Zhong'
Jiamang Wang² Alibaba Group
Weisi Lin 16
Nanyang Technological University (xi zhang, hanwei zhu, walin] edu. sg
Abstract
In this work, we propose a novel framework to enable diffusion models to adapt their generation quality based on real-time network bandwidth constraints. Tradi- tional diffusion models produce high-fidelliy images by performing fixed number denoising steps, regardless of downstream transmission limitations. However, in practical compression, leading to loss of fine textures and wasted computation. To ad- dress this, we introduce a joint end-to-end training strategy where the diffusion model is conditioned on a target quality level derived from available bandwidth. During training. the model learns to adaptively modulate the denoising process, enabling early-stop sampling that maintains perceptual quality appropriate to the target transmission condition. Our method requires minimal architectural changes and leverages lightweight quality embedding to guide the denoising trajectory. Experimental results demonstrate that our approach significantly improves the visual fidelity of bandwidth- wadaptt generations compared to naive early-stopping, offering promising solution for efficient image delivery in bandwidth- contsrtthh--ottttieeedd environments. Code is available at:
scenarios, limited bandwidth often necessitates heavy
Introduction
Diffusion models [3
37 40 have recently demonstrated remarkable capabilities in syn- thesizing high-quality images, significantly surpassing previous generative approaches such as GANs 100
43 15
47). Despite their impressive fidelity, deploying diffusion models in realistic cloud-to user applications introduces fundamental bottleneck: trans- mission bandwidth. In conventional scenarios, generated images undergo aggressive lossy compres- 55 before transmission to accommodate limited bandwidth. This cascaded approach-hhigh-qullll high--qulity image generation followed by subsequent compression- not only incurs redundant computational overhead but also significantly degrades perceptual quality, as the
36
2 19] and VAFS 21
38
12
sion 45 46 44 55 34
32 58
compression process often erases the intricate textures and fine details 24 g 56 carefully constructed by the diffusion model.
57
7
25
16 48
This motivates critical question: Can we directly integrate bandwidth- into the diffusion generation process, avoiding the inefficiency and perceptual quality loss associated with post- generation compression? Diffusion models inherently provide a natural mechanism for addressing this challenge. During sampling, these models progressively refine coarse structures into detailed, realistic textures through iterative denoising steps. Thus, intuitively, terminating the diffusion process early results in simpler, lower-detail images suitable for constrained bandwidth scenarios. However, naively reducing the number of diffusion steps typically produces suboptimal visual quality, as models trained for complete denoising trajectories are not optimized for early termination, leading to visual artifacts and poor perceptual coherence.
Corresponding authors.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Traditional Method
Lossy Compression
Quality Degraded
Instruction
O |||
Bandwidth Bottleneck
X Transmission Failed
Cloud
Images
Lossless Compression
BADiff (Bandwidth-Adaptive Diffusion)
Real-time Bandwidth
Instruction
НΣЛЛ I||I
Bandwidth Bottleneck
User
Cloud
Bandwidth- Bandwidth-Adaative
Lossless
Quality Preserved
Generation
Compression
Figure I: Comparison of traditional diffusion + compression pipeline (top) and the proposed BADiff framework (bottom). BADiff directly generates entropy-comee constrained images suitable for bandwidth- limited transmission, avoiding quality degradation in post-generation compression.
To effectively address this issue, we propose the Bandvidth-Adaptiee Diffusion Model (BADiff). novel diffusion model explicitly conditioned on target bandwidth constraints, formulated entropy targets. By embedding target entropy as an explicit conditioning input, our approach enables the diffusion model to adaptively modulate its denoising behavior. During training, the model is exposed to variable entropy constraints, allowing it to produce perceptually pleasing images even under reduced-step sampling. Furthermore, an entropy regularization loss ensures the generated images adhere closely to the bandwidth constraints, obviating the need for aggressive post-hoc compression. As illustrated in Figure [ the conventional diffusion pipeline relies on lossy compression to meet bandwidth constraints, often degrading visual quality, whereas proposed BADiff framework directly generates antropy-constraing outputs suitable for transmission without compromising perceptual fidelity.
Our proposed BADiff framework provides several advantages over existing cascaded and naive carly-stopping approaches. First, it significantly reduces computational overhead by adaptively terminating sampling, ensuring efficient inference. Second, by directly generating images meeting bandwidth constraints, BADiff avoids compression-induced artifacts, thus preserving perceptual quality. Third, our framework provides fine-grained, dynamic control over image quality based real-time bandwidth conditions, enhancing deployment flexibility in practical cloud-to-use applications.
We validate the effectiveness of BADif through extensive experiments comparing our method to strong baselines, including standard diffusion models with post-generation compression and naive carly-stopping approaches. Our results demonstrate that BADiff consistently achieves superior trade- offs among perceptual quality, computational efficiency, and bandwidth efficiency, underscoring the advantage of integrating bandwidth-awarenee directly into the generative modeling process.
Our main contributions be summarized as follows:
We introduce BADiff, the first bandwidth-addaee diffusion model explicitly conditioned target entropy constraints, directly addressing image synthesis for bandwiidth-constrained transmission.
We propose an entropy conditioning mechanism integrated into diffusion models, coupled with an entropy regularization loss, allowing adaptive and efficient generation under diverse bandwidth constraints.
We develop an adaptive sampling policy that dynamically determines optimal sampling termination, significantly reducing computational cost while preserving image quality.
Through extensive evaluations, demonstrate BADift's superior performance in perceptual quality, computational efficiency, and adherence to bandwidth constraints compared to conventional cascaded diffusion compression pipelines.

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2 Related Work
2.1 Diffusion Models
Diffusion models have recently gained significant attention due to their remarkable ability to generate high-quality images, surpassing traditional generative models such as GANs [TO] and VAEs [21] The foundational work of Ho et al. [13] introduced Denoising Diffusion Probabilistic Models (DDPMs), formalizing diffusion models as a parameterized Markov chain trained by variational inference to invert gradual noising process. Song et al. 43 further generalized the framework through Score- based Generative Models (SGMs), which unify diffusion models and score-matching approaches under cittiuuuus-tmee stochastic differential equation (SDE) framework. Recent works have extended diffusion models to various tasks beyond image synthesis, including video generation [15), text-to-image generation 37 40), and 3D synthesis [35].
2.2 Accelerated Sampling of Diffusion Models
Despite their nigh-quality outputs, diffusion models are computationally expensive due to the iterative sampling procedure required during generation. To mitigate this issue, substantial efforts have been made toward accelerating diffusion model sampling. DDIM [42] introduced deterministic sampling methods enabling fewer inference steps, significantly reducing computation. Further advances, including DPM-Solver [29] and FastDPM [22], have employed numerical methods inspired by ordinary differential equations (ODEs) shorten sampling times substantially while preserving generation quality. PNDM (28) introduces pseudo-numerical solver that treats the reverse diffusion ODE with high-order Runge-Kutta-stlee updates, enabling high-fidelity image generation in few as four forward passes. Knowledge distillation based methods [4] 31] reduce sampling steps by distilling knowledge from slower teacher models into faster student models. Alternative approaches involve adaptive step size selection [17] or latent space compression [39] to reduce computational
overhead. AutoDiffusion [26 further accelerates sampling via non non-uniform step skipping.
Unlike prior methods that optimize scheduling or model architecture, DDSM 49 introduces dynamic U-Net pruning to minimize redundant computations each step. This approach is complementary existing acceleration techniques. Related works include OMS-DPM (27), which optimizes model scheduling via predictorbbssed algorithms, and Spectral Diffusion (5)) which employs dynamic gat- ing for efficiency. While eDiff-I (3] uses multiple fixed-size expert models, StepSaver (52) proposes a step predictor to determine the minimal denoising steps required for high-quality generation, further improving efficiency. Moreover, adaptive methods such as AdaDiff (53) dynamically adjust inference trajectories, further enhancing efficiency by selectively allocating computational resources during sampling based on intermediate outputs.
2.3 Conditional and Controllable Diffusion Models
Diffusion models inherently provide powerful frameworks for conditional and controllable generation. Classifier-guidd -uiieed diffusion [9] utilizes gradients from auxiliary classifiers to steer the generative process toward desired attributes. However, training classifiers separately is often cumbersome and computationally expensive. Classifier-free guidance [4] resolves this issue by training diffusion models on conditional and unconditional inputs simultaneously, enabling flexible attribute control without additional classifiers. Latent diffusion models (LDMs) [39] further enhance controllability and computational efficiency by conditioning generation in latent spaces. Recent approaches like RePaint [30] have explored numerical control, such as region-based conditioning, to edit images interactively, although they do not directly address bandwidth constraints or entropy-aware generation. Our proposed BADiff model differs by conditioning generation directly entropy constraints, enabling explicit control over the generated image's 's compressibility and perceptual quality.
3 BADiff
We propose BADiff (Bandwidth-AAaptiie Diffusion), a conditional diffusion framework that integrates bandwidth constraints, formulated as target entropy values, into the diffusion sampling (see Fig. 2). Bififf aims to dynamically modulate generation to satisfy entropy constraints during generation, thus eliminating the need for post-hoc compression while saving computational cost.
3

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Clean Image X
Target Entropy HEarget
Sampled Noise
Entropy Embedding Network A
Denolsing E. L_demonise
Entropy Embedding h
Neural Entropy Estimator Hg
Entropy Regularization Loss L Lentropy
FILM Modulation
Predicted Noise Eg
Noisy latent X;
Forward Process
U-Net (Conditioned Denoiser)
Calibration
Reference Codec
Timestept
Reconstructed Image Kg
Loss C_catibration
Noisy latent
Policy Network
Stopping Probability P:
Stopping
Pollecyooss
f
Timestep 1
Offline Teacher Stop labels y/
E_stop
Target Entropy Hearger
Figure 2: Overview of the BADifT training framework. The proposed framework jointly optimizes image generation quality and bandwidth adaptability. The total training objective integrates four complementary losses: (I) the standard Denoising Loss Luemoise for reconstruction; (2) an Entropy Regularization Loss Centropy enforced by differentiable Neural Entropy Estimator Hş ensure the budget is met; (3) a Calibration Loss Cealibration that aligns the estimator with a Reference Codec; and (4) Stopping Policy Loss Lsop to train the lightweight Policy Network fo for adaptive early exiting.
3.1 Background: Diffusion Models
Diffusion models generate data by reversing forward process that gradually adds Gaussian noise. Formally, given clean sample Xo, the noisy latent at timestep t can be sampled directly via the reparameterization trick:
Vā Xn + VI- ā, E~ (O,
(I)
where is derived from fixed noise schedule. The generative process relies neural network (x,,, t) trained to predict the added noise e. The standard training objective minimizes the simple mean-squared error:
Leenosse Ex..,. [[le- ca (x,, +)] By iteratively removing the predicted noise starting from Xy (O, I), the model reconstructs the data distribution.
(2)
3.2 Entropy-Conditiones Diffusion Model
In standard DDPM, the reverse process refines noisy latents x, into clean image Xo through a Markov chain with Gaussian transitions Pe (x xx) = N(xx-1: (X,, models ignore external resource constraints (e. g. bandwidth). BADiff enforces the constraint by conditioning every reverse step on a target entropy budget Htarget E Rso-
(x,,t,, f), [x,x, f)). Such
Specifically, extend the reverse kernel to
Po (x,x111 X,, Harget) A x Mg (X Huaggt:; Eg (x t, Hraneet):
so that the predicted noise (or velocity) becomes ég = cx t, Hunget).
single scalar is not expressive enough for deep conditioning, therefore we map Hurger into d-dimensional vector via learned entropy embedding network
h (H((Hurgg)) E Rd
(4)
where uh, IR Rd is an MLP with parameters 77. Throughout the paper fix d 128.
Let g()) be the usual sinusoidal timestep embedding. For every residual block of the UNet we form a hybrid modulation
(t, Hearet) g(t) + w h.
(5)

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and add gi to the block's ' activation just before the first convolution (equivalent to additive FiLM). Here w E gexd is learned per-block and is the channel width. Consequently every output of the denoiser, e ea(x;, t, Hurger), is explicitly conditioned on the entropy budget.
This design keeps the overhead negligible (< 0.1% additional parameters) while giving the network continuous control "dial" over the amount of detail it should recover, enabling BADiff to generate images whose bit-rate naturally matches the specified bandwidth.
3.3 Entropy Regularization Loss
Conditioning the reverse process on an entropy budget is necessary but not sufficintt: the model could still output images whose empirical entropy (exceeds the target. To make the constraint active during learning we attach an explicit penalty that is differentiable w.r.t. both the image and the network parameters.
Let Xo = (X,, t, Harges) be the reconstructed clean sample predicted at time-step t. We introduce Lentroyy = max (0, (Xo) Hurget)
(6)
where H.) is a differrentaabe neural entropy estimator parametrized by ó and jointly optimized with 0. The hinge form ensures that no gradient flows once the sample entropy is already below the budget, so the optimizer focuses on over- budget cases.
Differenniable neural entropy predictor. In learned image compression 5 34 33 the entropy model predicts a pixel-wise conditional distribution Pal (r c.,) given causal context c, (e.g. neigh- bouring pixels or hyper-prior) and converts it to code-length via log, Ps. We adopt the same principle for BADiff.
For each spatial position E Ω the entropy network Eg outputs continuous parameters O, (nu, of a discretized logistic distribution [5]:
polaa c.)) = Di(aui 1 = phs o = oo))
The expected code-length (bits-per-pixel) for an image x therefore
Hx(x)
Σ loga logap<(2 lc),
(8)
[
which is fully differentiable w.r.t. both 0, and the upstream activations that determine c.; hence gradients flow into the UNet.
and construct C. from two sources: (i) hyper-prior predicted by a lightweight conv-net over x, and (ii) an auto-regressive causal context of previously decoded pixels (realised masked convolutions).
Context extraction. We follow
Gradient properties. Because the discrete logistic PMF is analytically differentiable w.r.t. μ. and log ou. Eq. (8) supplies exact gradients: Ve, Vo. inz Vo., Logpo(z,, c.)). Hence the entropy
constraint is enforced and-to-end, unlike histogram- based surrogates that require straight-through tricks.
Self-supervised calibration of Fig. Although Ee trained jointly via the hinge loss Lents benefits from an auxiliary signal that anchors its probabilities to a known codec. To this end we derive pixel-wise targets (k) from a reference end-to-end optimized image codec. We then minimize the spatially averaged cross-entropy
Lealibration
(k) logz polk | cc.)),
Ω
which is equivalent (up to a constant) to the KL-divergence (R P&). This term calibrates the logits toward realistic code-lengths without over-regularizing.
Because Ho is differentiable, the model learns a direct mapping from an entropy budget to the statistics of its output, which empirically accelerates convergence and yields tighter adherence the target bandwidth than heuristic early stopping.
We use "entropy" shorthand for the expected code- (bits fets-per-pixel] after entropy- -oadyyy-oonngggoooo stage.
5

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3.4 Adaptive Sampling Policy
Let TE (I....,T) denote the (random) stopping time which sampling terminates and the current latent x, is decoded to the final image Xy. Ideally we would like to choose 7 so as to minimize the total cost
C(T)
{(x)) +
(xxo, Xrer)
(10)
eatropy
distortion
compute
where & is the entropy predictor (-)-), D is perceptual distortion (e.g. LPIPS to the reference x and 8, y>0 0 weigh quality vs. runtime. Brute-fore force evaluation at all impossible during inference,
so we approximate with lightweight classifier that decides on the fly whether to proceed.
Policy network. We introduce small MLP-based policy network fo: : Rd X that outputs the stop probability
Pt Solzes i, Hurget)
Ze
7u Σ [u] E
(11)
where 2, is spatial mean-pooled latent feature (h, are height/width, d channels). Sampling continues iff a Bernoulli draw b, ~ Bernoulli(1 - pp) returns 1. Thus the stopping time is T min{t b, V1
Supervised self-distillation. We generate teacher stop-labels offline: run a long-step sampler, measure the cost C(t) at each step and set
= L[((t) S min C(s)].
(12)
$2t
Hence y/ = 1 iff step is sufficient; earlier steps are labelled O. The policy is trained jointly with BADiff via
Laup E, BCE( pt)].
(13)
where BCE is binary cross-entropy. Gradients back- pack-propagate through pt but not through the discrete Bernoulli sample (stop/no-stop), ensuring stable training.
Inference procedure. During sampling we evaluate Pt at each step: if Pt 2 Tih (Tu = 0.5 by default) terminate and decode x,; otherwise we proceed to 1. Because the policy is only several layer MIP over 2, and (1, Hurret), ,, the additional runtime overhead is negligible (< 0.3 ms per
step on RTX 4090). Empirically ($4.3) BADiff stops about 50% earlier low-bandwidth budgets
while keeping LPIPS and FID constant, demonstrating the benefit of the adaptive sampling policy.
3.5 Training and Sampling
The full BADiff objective merges four complementary loss terms: (i) the standard denoising loss from DDPM, (ii) the entropy hinge that enforces the bandwidth budget, (tii a calibration loss that aligns the learned entropy model with reference codee, and (iv) stopping-polin loss that teaches the lightweight classifier when to terminate sampling. Formally,
L Ex cg(X,, t,, H marget)) [ A max(0, (x( H magget)
Cammise
Lamorr
(14)
+ Adal
Dki(gul
+ Astop EB[ fo t, H
Ω
wen
Cuv
Cexitration
During training we randomly draw Hurget ( Huax) to expose the network to broad range of bandwidth budgets, allowing it to generalize to unseen conditions. At test time user-specified bitrate is converted to an entropy budget Hurget- Conditioned on this value, BADiff starts from Gaussian latent and runs the reverse process. After each step the policy network fø(x,, L, Hunge) outputs a stop-probability; sampling terminates as soon as the probability exceeds a threshold 7h (0.5 by default).

---

Algorithm BADiff Training
Algorithm' 2 BADifI Sampling
1: repeat
Require: target entropy Hurger 1: XT ~ NNO..)
Xo ~ (
3: Hurge ~ (4(miin: Mmax)
2: for 1 T T...., do
4:
~~ U(1..... T} E~NN0,
3: Eg 4- Ex Hurge
5:
VaxXa + VI- are
4:
XI-1 Vaz (xi VT-re Eo) + 0:2,
Eo F ca ca(x;, t, Hugar)
NO,, [)>11
7: Xo + go (xt, Huma)
5:
if (xt-111 1, Hurga) STOP then
COEN = |e 66-é6ll Eoll2
6:
break
CETT = max(0, (x( H Hures)
7: end if
10:
CCAL কŪं Euen DKL(TN ( cu))
8: end for
9:
return X Xt-1
11:
Generate teacher label 3++
12:
Pe < (o( Hurge)
Runtime Notes:BADiff typically halts 30% % earlier than fixed-step sampler under low bandwidth budgets, cutting inference time with minimal perceptual loss.
13:
ESTOP = BCF Pt)
14:
= LOIN + LINT + LeA LxtOr
15:
Update [0, o) + {0, 00 (C)
16:
until converged
Algorithm|] summarises the entropy-conditioned training loop for BADiff. Each iteration first draws a clean image Xo and random entropy budget Harget, corrupts the image to timestep and lets the UNet predict the noise éş as well as reconstruction &o. The total loss combines the respect
usual denoising objective with an entropy penalty that encourages the reconstruction the bandwidth constraint. During inference (Algorithm{2) we start from pure Gaussian noise and iteratively apply the reverse update conditioned on the same entropy target. lightweight policy network fø monitors the latent at every step and terminates sampling as soon as the estimated entropy meets the budget, thereby saving computation while preserving perceptual quality.
4 Experiments
We empirically verify that BADifT fulfils its two key promises: (i) faithfully respecting user- specified entropy budget across a wide range of bitrates, and (ii) achieving this while simultaneously preserving image quality and reducing inference cost. To this end we benchmark BADiff on three standard umage-generatien datasets under multiple bandwidth regimes and compare it with strong compression-basee and carly-stopping baselines. We further present ablations that isolate the impact of each model component (entropy hinge, calibration loss, stopping policy) and provide qualitative visualisations that highlight BADiff'ss ability to degrade gracefully as bandwidth tightens.
4.1 Experimental Setup
Datasets. We train and evaluate on three standard diffusion benchmarks CIFAR- 10 23 CELEBA HQ [18), and LSUN- CHURCH/BEDROOM [51] All splits and preprocessing follow the original
DDPM protocol B 42
Baselines. The experimental comparison is organized around two diffusion backbones and several post-generation compression strategies. We adopt backbones: (i) DDPM-IK-the original
pixel-space UNet with 1 000 reverse steps [13] : (ii) LDM-200-4 latent UNet operating on 64x
compressed representations with 200 steps [39] For each backbone we two generic ways of
meeting bitrate constraint:
Cascade (Diflusion-CCodec)) Run the sampler to full convergence and then compress with BPG (6] or a learned image codec (LIC) [8]. This "generate-fite compress-later pipeline mirrors current cloud rendering practice and is our primary point of comparison.
Naïve Early-Stop: Truncate the sampler to the smallest such that the compressed output (BPG) satisfies the target bpp. This reveals the benefit of early termination without retraining the network.
We also benchmark two state-of-thed -ort----ttth-tttt- acceleration techniques that reduce the sampling cost without any explicit bitrate control: (i) the PNDM pseudo-numerical ODE solver (28) and (ii) the second-order DPM-Solver 229. Both are run with their default step counts the same backbones.
7

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Table FID on three datasets at three bitrate budgets for both backbones. DDPM uses 1 000 steps; LDM uses 200 steps. Lower is better.
CIFAR-I0
CELEBA-HO
LSUN
Backbone
Method
Low
Med
High
Med
High
Low
Med
High
DDPM 13
BPG
6
15.2
9.1
5.8
28.5
16.2
10.9
25.7
14.0
8.7
DDPM 13
LIC
8
13.6
8,4
5.3
25.3
14.5
9.4
22.8
12.2
7.5
Early- Stop
LIC
8
22.9
15,5
11.6
35.0
21.4
16.3
31.9
19.9
13.2
DDPM-IK
PNDM 28
LIC
18.1
12.6
9.4
30.4
18.9
13.7
27.3
16.4
11.7
DPM-Solver
29
LIC
8
17.8
12.3
9.1
29.8
18.1
13.1
26.5
16.0
11.3
BADifT
11.4
7.1
4.4
21.7
11.8
7.4
19.6
10.0
5,8
LDM
BPG
6
10.2
17.8
11.8
27.5
15.3
9.5
LDM
8
15.6
9.3
5.9
27.2
16.0
10.3
24.6
13.7
8.1
Sarly-Stop-1
LIC
24.2
16.6
12.1
37.3
23.1
17.0
33.4
20.8
14.0
LDM-2000
PNDM 28
1.C
19.9
13.4
10.0
31.8
20.2
14.4
28.9
17.8
12.2
Solver
29
LIC
S
19.2
13.1
9.7
30.9
19.6
13.9
28.1
17.4
11.8
BA
12.6
7.9
4.9
13.0
8.5
20.8
11.3
6.4
Bandwidth budgets. To mimic realistic mobile and desktop links we adopt three bitrate intervals that common in the learned compression literature: (i) Low (0.2-0.5 bpp): = 25-66 kB for 256² low-end 4G or satellite connections where aggressive compression mandatory. (ii) Medium (0.5-1.0 typical of standard 5G Wi-Fi transmission and roughly matches JPEG quality factors 50-75. (iii) High (0-.0bpp)) near-lossless quality for desktop viewing; permits fine textures but still below PNG size. For every training batch we draw Hurget (0.2, 2.0) so the model experiences the full spectrum during optimisation, while at test time we report results the three disjoint intervals above.
RGB image, representative
Evaluation metrics. We report FID IT. LPIPS [54], empirical bitrate per pixel (bpp), and average inference time (ms) RTX-4090 GPU. Together, FID and LPIPS assess perceptual fidelity, the bitrate quantifies adherence to the bandwidth budget, and inference time captures the computational advantage of early termination afforded by BADiff.
4.2 Quantitative Results
Table Takeereeee reports the FID scores (lower is better) of all methods across three datasets: CIFAR-10 10,
CELEBA-HOQ and LSUN, under three bandwidth budgets (Low: 0.2-0.5 bpp. Medium: 0.5-1.01 bpp.
High: 1.0-2.0 bpp). using both DDPM-IK and LDM-200 as backbones. Across the board, BADiff' achieves the best FID scores in all settings, outperforming both post-hoc compression baselines (Cascade BPG / L.C)) and accelerated solvers (PNDM, DPM-Solver). On CIFAR-10, for example, BADiff reduces FID from 15.2 (DDPM+BPG) 11.4 in the low-rate DDPM setting, and from 17.3 (LDM+BPG) to 12.6 under the LDM backbone. Similar improvements are observed on CELERA-HQ and LSUN, where BADiff often outperforms even the strongest cascade baselines by large margin. Moreover, early stopping baselines (with LIC) exhibit significantly worse FID despite matching bitrates, confirming that simply halting the sampling process without training for intermediate-step outputs yields inferior results.
4.3 Inference Speed
We report end-to-end sampling latency (ms/image) on CIFAR-10 (32 x 32) using an NVIDIA RTX-4090 GPU. Each value is averaged over 1 (00 test samples following 50 warm-up iterations. Table presents the results under three bitrate regimes for both DDPM-IK and LDM-200 backbones. BADIII consistently reduces latency compared to the Cascade baselines (Diffusiin + Compression). particularly in low- and medium-rate settings. On DDPM-1K, 1k, BADiff achieves 1.7x speed-up over Cascade+LIC at low bitrate (65 ms vs. 115 ms), and 1.5x at medium bitrate (78 ms vs. 115 ms). Similar trends are observed with LDM-200. where BADiff is up to 1.7x faster than the cascade pipeline at low bitrate (27 ms vs. 47 ms). While slightly slower than Early-Stop due to its adaptive decision-making, BADiff offers significantly better FID (T) making it more desirable trade-off between speed and perceptual quality.
8

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Table 2: Per-image inference time (ms) CIFAR- 10 under DDPM-IK and LDM-200 backbones across different bitrate regimes. Lower is better.
Table 3: Ablation study CIFAR-10 (DDPM backbone) under the low bitrate regime (0.2 0.5 bpp).
DDPM-IK Med.
LDM-200
Variant
FID,
A bppl
Timel
Method
High
Low
Med.
High
w/o Cond.
13.1
0.038
64
Cascade + BPG
110
110
110
43
43
43
Cascade + LJC
115
115
115
47
w/o Hinge
16.2
0.055
65
Early-Stop
75
92
31
w/o Cal.
18.6
0.043
65
BADiff
34
Full BADiff
11.4
0.021
65
Table 4: High-resolution evaluation on 5122 and 1024² images under realistic bitrate constraints, comparing BADiff with Liffusion+LIC baselines. Both FID and inference time (ms) reported.
Resolution
bpp
Metric
DDPM+LIC
PNDM+LIC
BADiff
0.4-0.6
FID
8.45
7.90
6.85
5122
Time (ms) 4
121.3
98.6
64.1
10243
0.8-1.2
FID
21.5
20.1
17.8
Time (ms)
228.7
192.5
145.6
4.4 Ablation Study
To understand the contribution of each design component in BADiff, we conduct a controlled ablation on CIFAR-IO 10 under the low bitrate regime (0.2-0.5 bpp). Each variant is retrained for 800 k iterations using the same optimizer settings, and evaluated using three key metrics: FID, A bpp (absolute bitrate deviation from target), and average inference time (ms/image) on RTX-4090 GPU.
Ablation variants. We evaluate three reduced versions of BADiff, each with one component removed: (i) w/o Conditioning: removes the entropy embedding from the UNet, disabling bitrate- aware generation. (ii) w/o Hinge Loss: sets Aen = 0, removing the entropy penalty during training. (iii) w/o Calibration Loss: sets Acal preventing alignment between predicted entropy and coded length derived from an end-to-end optimized codec.
Analysis. Removing the entropy conditioning impairs the model's ability to modulate detail based on bitrate, resulting in a higher FID (+1.7) and worse bitrate adherence (+0.017 bpp). Without the hinge loss, the model ignores bandwidth constraints altogether, producing the largest deviation from target bitrate (0.055 bpp) and the worst FID (16.2). Disabling the calibration loss increases bitrate error (+0.022 bpp) while slightly degrading FID (+7.2), indicating that codec alignment improves control without compromising perceptual quality. Overall, only the full BADiff configuration balances visual fidelity, precise entropy control, and efficient inference. In terms of inference time, all ablated variants retain comparable speed to the full BADiff (65 ms), since the adaptive stopping policy remains enabled. This confirms that the primary contributor computational efficiency is the adaptive sampling policy mechanism and entropy-aware generation, rather than any single auxiliary loss. Overall, only the full BADiff configuration balances visual fidelity, precise entropy control, and efficient sampling.
4.5 Scaling to High- Righ-Resslutton Images
To address the scalability concern, we perform new experiments at higher resolutions to verify that (i) conditioning on a single scalar entropy target remains valid scale, and (ii) BADiff continues win both in fidelity and runtime. In practice, streaming systems typically assign a single bandwidth per frame, leaving spatial allocation the codec; BADiff mirrors this regime via global entropy target with differentiable entropy-aware allocation, encouraging adaptive texture reduction in less salient regions while preserving important details. We retrain BADiff and two baselines (DDPM+LIC and PNDM+LIC) on 512² and 1024² images under realistic bitrate budgets. Table shows that BADiff consistently achieves lower FID and faster inference across resolutions (e.g.. at 5122 FID drops from 7.90 - 6.85 and runtime reduces 98.6ms + 64.1ms; at 1024 FID drops from 20.1 - 17.8 and runtime reduces 192.5ms - 145.6ms). These results confirm that BADiff seales favorably to high-resolution generation under bitrate constraints.

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Table 5: Comparison of BADiff with diffusion+LIC baselines on Stable Diffusion text-to-image
generation across low (0.2-0.5 bpp). medium (0.5-1.0 bpp). and high (1.0-2.0 bpp) bitrate regimes.
Method
Low (0.2-0.5 bpp)
Med. (0.5 1.0 bpp)
High (1.0 bpp)
Cascade (SD+ BPG)
33.5
21.4
14.8
Cascade (SD LIC)
30.7
19.2
13.1
Early-Stop + LIC
41.8
27.5
18.0
DPM-Solver (20) + LIC
36.5
16.3
BADiff (ours)
26.1
16.2
11.0
Table 6: One-time cost of generating teacher labels across datasets and resolutions, measured on an RTX 4090. The labels are computed once offline and then cached; training never re-runs the diffusion chain. The cost is reported both in absolute GPU-hours and as a fraction of single training epoch.
Dataset
Resolution
GPU-hours
Relative to training epoch
CIFAR-10 10
32 X 32
0.8
5%
CelebA-HQ
256 x 256
3.5
2 6%
COcO-va12017
512 x 512
10.0
R3 8%
4.6 Extension to Text-to-lmage Models
To explore the applicability of BADiff beyond unconditional generation, we conduct preliminary experiments text-to-image setting using Stable Diffusion as the base model. BADiff's entropy- conditioning mechanism is fully compatible with conditional diffusion, enabling bitrate-controlled generation without modifying the text-conditioning pathway. We evaluate BADiff against several diffusion+LIC basclines under low, medium, and high bitrate regimes. As shown in Table BADiff consistently achieves lower FID across all bitrate ranges, indicating that BADiff effectively preserves visual quality even under tight bitrate constraints in text-conditioned generation.
4.7 Teacher Label Generation
To clarify the cost of teacher label generation, we emphasize that teacher labels are created once per image in an offline pee-proesssing stage, not during each training iteration, incurring negligible runtime overhead. First, we perform a single long diffusion run per training image (e.g., 1000 DDPM steps or 200 LDM steps) to obtain the entropy trajectory C(I) and derive binary labels as in Eq. 12 For CIFAR-10 on single RTX 4090, this entire offline step takes roughly 0.8 GPU-hours amortized over 800k training steps. Second, once computed, labels are cached and reused without re- re-running any diffusion chains; during training only a small MLP policy head is evaluated (< 0.1% of UNet FLOPs). Third, the cost remains small even at higher resolutions such 512 512, amounting only 5-8% of the time needed for one training epoch, as summarized in Table These results demonstrate that the teaeher-label strategy is efficient and scalable without affecting training throughput.
Conclusion
We presented BADiff, the first diffusion framework that generates images directly under an explicit entropy (bit-rate) budget rather than relying on post-hoc compression. By conditioning every reverse step on a target entropy embedding, adding a differentiable entropy-hings loss, and introducing an adaptive stopping policy, BADiff produces handwidth-complian images while preserving perceptual quality and reducing inference cost. Extensive experiments on three standard datasets show that BADiff surpasses strong cascaded and carly-stopping baselines in FID and LPIPS at all bandwidth levels and achieves up to a 2x runtime speed-up under tight constraints.
Limitations & future work. BADiff currently targets spatially uniform entropy budgets and images up to 2562 resolution. Future extensions include spatially varying bit-allocation, integration with faster solvers such as DPM-Solver or PNDM at higher resolutions, and applying the same principle to video diffusion models where bandwidth constraints are even more stringent. We hope BADiff will inspire further research resource-aware generative modelling for real-workh deployment.
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Acknowledgements
This research is supported by the RIE2025 Industry Alignment Fund Industry Collaboration Projects (IAF-ICP) (Award 12301 E0026), administered by STAR,, as well supported by Alibaba Group and NTU Singapore through Alibaba-NTU Global Sustainabiility CorpLab (ANGEL). This work also supported in part by the National Natural Science Foundation of China (No.62301313).
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Technical Appendices and Supplementary Material
A
Theoretical Justification of Entropy-Constraied Diffusion Models
Here we provide theoretical justification for the proposed entropy-constraine diffusion model by deriving its conditional reverse distribution. We first revisit the standard formulation and subsequently derive our culoopy-conditione variant.
A.1 Standard Reverse Diffusion Formulation
In the standard DDPM framework 1 the forward diffusion process gradually injects noise into the data Xg. following the Markovian formulation:
((xi.T Xo) [xx(xxxx--),
(15)
where each transition step is modeled as a Gaussian:
gxx, x;-1) = (Xxx; 10 (1 -a)))).
(16)
The reverse denoising distribution aims invert the forward process by progressively removing the noise:
T
(xoo)) = p(xr) II
(17)
t=1
Each reverse step distribution parameterized as:
Po (x = |xxx-1; t). (x,,,))) t)).
(18)
A.2 Entropy-Consstrined Reverse Diffusion Derivation
In BADiff, explicitly condition target entropy level Hunga, leading to the modified reverse conditional distribution:
pa (2 1, Xx, Heargr)
po (x,- Xty Haarget)
(19)
Po (Xe: Hurres)
By applying Bayes' rule and assuming conditional independence between Hurget and earlier states given X4, we simplify follows:
Po Hungee X2, X² (x)x(xx1112/
Po (x Nx, Huaga)
(20)
Po (Haggtt xxe)
2 po Harget Xt )ool Xx- (x.)
(21)
po (Hangal (x+))
Here we explicitly model the conditional distribution po Hurger xx-1) as a differentiable entropy estimator H (x.-)) The conditional entropy-based term can be approximated as:
(- Aemt max(0, Hx(x:-)) Hurget))
Hurger (x- sJ exp
(-2
(22)
where Aem is hyperparameter controlling the strength of the entropy constraint.
A.3 Interpretation Regularized Reverse Process
Combining these results, we rewrite the entropy-conditioned reverse step as Gaussian distribution with regularized mean:
(- Aent
Pe (xxxx [Xc; Harger) ox po (xt- (x:) exp
(-2 2
max(0, Ho (x:-1) Haapor)))
(23)
22

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Thus, the entropy constraint effectively acts soft regularizer, guiding the reverse process toward latent states x whose corresponding entropy estimate meets the target. This regularization not only provides theoretical grounding for the proposed entropy loss but also justifies our observed improvement bitrate control and image quality.
These derivations rigorously establish how entropy conditioning naturally emerges as a constrained form of reverse denoising diffusion, providing both theoretical validation and insights into the BADiff training objective presented in the main paper.
B Gradient Analysis of Entropy Loss
To better understand the optimization behavior of BADiff under entropy constraints, we analyze the gradient of the entropy loss with respect to the predicted image Xy. The entropy loss is defined as:
Lent max(0, (%o) Hurge);
(24)
where He is a differentiable neural estimator of image entropy.
Gradient Derivation.
The subgradient of Lent with respect to Xy is given by:
V H (8o), 00
if H&(Xo) > Hunget, otherwise.
%o Cent
(25)
This reveals that the entropy loss one-sided: it only contributes gradient signal when the predicted entropy exceeds the target. Below the threshold, the loss becomes flat and the gradient vanishes. This prevents the model from overcompressing its outputs when already under budget, ensuring that perceptual fidelity is not sacrificed unnecessarily.
The gradient V xx Ho typically promotes spatial smoothing in regions with high entropy-suce edges or textures textures- encouraging the model to selectively suppress fine details that contribute the most to bitrate. Since the penalty is activated only when the entropy is above budget, BADiff naturally learns modulate detail in a targeted and efficient manner, preserving structure when possible and discarding complexity only when required.
Interpretation.
This analysis aligns with our qualitative findings: BADifT gracefully degrades low-bitrate regimes while maintaining strong visual coherence, and achieves tight bitrate adherence without harming perceptual quality.
C Robustness to Entropy Predictor Approximation
The accuracy of the differentiable entropy predictor Ho plays critical role in BADiff's training. However, the predictor need not match the true codec exactly be effective. Here, briefly justify why approximate entropy guidance still yields reliable bitrate control.
Let (X)) denote the true entropy measured by black-box codec (e.g., BPG), and Hx())) the neural approximation. Suppose the approximation error is bounded:
Ho (Ko) - (inu((Xo) S
(26)
Then, the deviation from the target H also remains bounded:
(x0))
Hurger
H
(27)
Thus, if H& slightly underestimates entropy, the training loss compensates by encouraging more conservative image generation. This explains why BADiff retains bitrate adherence even with an imperfect H., as also shown in the ablation study.
Future work could explore jointly training Hg with contrastive or reinforcement signals to further narrow the approximation gap.
23

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D
Complexity Analysis
We analyze the computational complexity of BADiff compared standard diffusion baselines and fast solvers, focusing on the number of forward passes, memory usage, and latency scaling with respect entropy budget.
Step Complexity.
Let I" denote the total number of sampling steps (c.g., 1000 for DDPM, 200 for LDM), and T the number of steps actually executed under BADiff's ' adaptive stopping policy.
LDM (fxxedlengtth: always performs T forward UNet passes.
BADiff (adaptive): performs f leads to earlier termination.
steps on average. / varies with target bitrate; lower bitrate
Fast Solvers (e.g., PNDM): typically fixed low number of steps, but quality suffers without entropy control.
For UNet of cost O(C) per step, the total cost becomes:
COSTRADiE = u. O(C), vs. CosIcascade = T O(C) + Codec overhead.
Entropy Modules. BADiff introduces three lightweight modules: the entropy embedding MIP, the entropy predictor Hg. and the stopping policy network fe-
Entropy embedding: MLP layers with 256-dim hidden width, used once per step; negligible overhead (<1%).
Entropy predictor: small CNN (~0.3M parameters), used during training only; ignored during inference.
Stop policy: 3-layer MLP evaluated at each step; cost comparable to single linear layer.
Memory Usage. BADiff's memory footprint on par with standard diffusion models. Unlike guidance-based methods (c.g., classifier guidance) that double the forward pass, BADiff avoids any additional gradient computation during inference.
Latency Scaling. Assuming average Î < BADiff reduces latency linearly with the number of effective steps. For instance, at low bitrate (0.2-0.5 hpp), we observe a 1.7x reduction in wall-clock time over Cascade with DDPM.
Summary. BADiff achieves bitrate adaptivity with only minimal computational overhead. Its complexity scales sublinearly with bitrate, and its modular design allows plug- alug-and-per and-play integration into existing UNet-based diffusion pipelines.
E Implementation Details
provide full training and evaluation details for all experiments in this paper.
Training schedule. Each model is trained for 800,000 iterations using batch size of 64 images per GPU. We use automatic mixed precision (AMP) to accelerate training and reduce memory consumption. Training takes approximately 3 days NVIDIA RTX 4090 GPUs for the DDPM backbone and 2 days for the LDM backbone.
Optimizer and scheduler. We adopt the Adam optimizer 20 with default coefficients B1 =190.9. 32=0.999. The learning rate set to 1 x 10-4 and kept constant throughout training. No learning rate decay warmup is applied. Gradient clipping is used with max norm of 1.0.
Sampling parameters. For DDPM, we use 1.000-step linear beta schedule as in the original DDPM implementation [33 For LDM, we follow 39 and use 200 steps with cosine noise scheduling the latent space. At inference time, the sampling process is governed by the entropy-aware stopping policy, which dynamically terminates carly based the predicted bitrate.

---

Hardware and software. All experiments are run on NVIDIA RTX 4090 GPUs with 24GB VRAM each. We use PyTorch 2.1.0 with complee enabled for maximum inference speed, and CUDA version 11.8. The entropy-aware modules are implemented in native PyTTorch without any custom CUDA kernels. Experiments are managed via Accelerate and Weights Biases for reproducibility and logging.
Codec baselines. For BPG, we use the official reference implementation compiled with 1ibbpg-0 0. 9. For learned image compression (LIC), we adopt the pre-trained model of Cheng2020 [8] from CompressAI. BPG codee experiments all run on CPU and LIC experiments all run on GPU, with the output bitrate measured post-compression in bits-per-pixe (bpp).
Model Architectures
This section describes the architecture details of all core modules in BADiff, including the UNet backbone, entropy conditioning MLP, stopping policy network, and differentiable entropy predictor.
UNet Backbone. We use modified version of the standard UNet architecture introduced in DDPM [3]. The configuration as follows:
Downsampling path: 4 resolution levels with channel counts [128, 256, 512, 512]. Each level consists of two residual blocks (with GroupNorm SiLU) followed by downsampling layer (stride-2 convolution).
Bottleneck: 2 residual blocks with 512 channels and an attention layer at the lowest resolution (8x8 for CIFAR-10).
Upsampling path: mirrors the downsampling path with learned upsampling (transposed conv), residual blocks, and attention at the second-lowest resolution.
Timestep Entropy Conditioning: the diffusion timestep and entropy target are embedded sepa- rately (see below) and added to each residual block via FiLM modulation.
Entropy Embedding MLP. The target entropy Hurga is a scalar projected into high-dimensional embedding via:
Input: sealar entropy in [0.2, 2.0].
Architecture: 3-layer MLP with hidden sizes [128, 256, 256], SiLU activations.
Output: embedding e E g256
Integration: the embedding is fused into each UNet block via FiLM: y = h 8, where () are predicted from e.
Stopping Policy Network. The policy module fo is compact classifier; Input: pooled mid-layer UNet features, timestep embedding, and entropy embedding.
Architecture: 3-layer MLP with widths (256, 128, 2), SiLU activations.
Output: stop/continue logits via softmax.
Training: supervised with labels from offline oracle policy.
Differentiable Entropy Predictor Eg. The entropy estimator is CNN-based with soft binning: Input: predicted image Xg-
Backbone: 4 conv layers with channels [32, 64, 64, 128], kernel size 3x3, stride 1, GroupNorm.
SiLU.
Context modeling: 1 masked 5x5 convolution.
Output: per-pixel logits over K-64 soft histogram bins.
Usage: softmax probabilities p& (A:
x(u]) used for entropy loss.
G Hyperparameters
Table lists the main hyperparameters used throughout training for all BADiff models, unless otherwise stated. We adopt the default settings from DDPM [13 for the optimizer and noise schedule, and perform minimal tuning to isolate the effects our proposed components. The entropy-related weights dent. Acat, and Astp are set via coarse grid search on CIFAR-10 validation splits.
25

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Table Key hyperparameters.
Hyperparameter
Value
Learning rate
10-4 Aent = 0.1
Entropy hinge weight
Calibration loss weight
Acal = 10-3
Stopping loss weight
stop 10-2
Batch size
128
Entropy embedding dimension
128
Training iterations
800 k
H
Broader Impacts
Our work introduces new class of generative models that explicitly adapt image synthesis to band- width constraints, enabling more efficient and controllable generation under limited communication resources. By jointly optimizing generation quality and bitrate compliance, BADiff may benefit wide range of real-world applications where bandwidth a bottleneck- as mobile inference, telemedicine, satellite imaging, and cloud rendering.
On the societal side, more bandwidth-efffiienn generation could reduce carbon emissions associated with media transmission and enable broader accessibility in under-connected regions. At the same time, like other generative models, BADiff could potentially be misused produce banddiddhhh synthetic media for malicious purposes, such as misinformation or surveillance. We encourage the research community to pair technical advances with rigorous content provenance and auditing mechanisms.
Finally, our approach is orthogonal existing safety or fairness measures in generative modeling. BADiff does not inherently mitigate or amplify dataset biases, but it can be combined with bias-aware training strategies fairness constraints needed in deployment contexts.
26


Reviews:
[{"review_id": "A9kME6C92R", "reviewer": "Reviewer_NzT6", "summary": "BADiff  is a novel framework designed to make diffusion models aware of network bandwidth constraints during the image generation process. The core idea is to condition the diffusion model's denoising process on a target entropy level, which is derived from the available bandwidth. This allows the model to generate images of a quality appropriate for the transmission channel, thereby avoiding the computational waste and quality degradation associated with the standard practice of generating a high-quality image and then aggressively compressing it.", "questions": "1. Could the authors provide insight or preliminary results on BADiff's relative performance when the baseline is not a 1000-step DDPM/200-step LDM, but a fast DPM-solver running in, for instance, 20 steps?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "## Strengths:\n\n- It's quite interesting and practical to perform research on the mismatch between high-fidelity generation and bandwidth-limited transmission. The proposed solution of integrating bandwidth awareness directly into the generative process is inspiring. The problem formulation is clear, and the potential impact on cloud-based AI services is substantial. \n- The methodology is grounded in theoretical underpinnings, with explicit integration of entropy conditioning into the reverse diffusion process and a joint loss formulation that enforces adherence to bandwidth constraints through a differentiable entropy estimator and regularizer.\n- Authors use two different backbones (DDPM and LDM) to demonstrate the general applicability of the method. The ablation study effectively validates the contribution of each component of the proposed framework (conditioning, hinge loss, calibration loss). \n\n## Weaknesses:\n\n- The experiments are conducted on relatively small datasets or resolutions.  While the authors acknowledge this limitation,  it is not guaranteed that the method will scale effectively, as generating fine details in high-resolution images might be difficult to control with a single scalar entropy target.\n- In line 209, the \"teacher\" labels are generated by running a full, long-step sampler and finding the optimal stopping point offline based on a cost function.  This seems to imply that for every training sample, a full generation is required to create the label, which would cost lots of computation. Are these labels pre-computed for a fixed set of images or generated in real-time in some efficient manner?\n- Besides the quantitative metrics such as FID, LPIPS, and runtime, can authors provide some user studies or task-specific downstream evaluation about the application potential of BADiff?", "was_revised": true, "final_justification": "After reading the authors' rebuttal and the other reviewers' comments, I think my concerns have been adequately addressed. I would like to keep my score.", "rebuttal": "### **[W1, scaling to high-resolution images]**  \nWe thank the reviewer for raising this important point. To address the concern regarding scalability, we conducted new experiments at significantly higher resolutions. Below, we (i) justify why conditioning on a single scalar entropy target remains effective at scale, and (ii) provide new empirical evidence on $512 \\times 512$ and $1024 \\times 1024$ benchmarks demonstrating that BADiff continues to outperform strong diffusion+LIC baselines in both fidelity and runtime.\n\n1. **Validity of global entropy conditioning.**  \n   In real-world streaming systems, a single bandwidth budget is typically assigned per frame, with spatial bit allocation handled internally by the codec. BADiff mirrors this setup by conditioning the generation on a global entropy target, while allowing the model to learn spatially-aware allocation through the differentiable entropy hinge loss. This encourages adaptive texture reduction in less salient regions (e.g., backgrounds) while preserving fine detail in important areas. Figure A.1 in the supplement confirms that this behavior generalizes well to $1024 \\times 1024$ images.\n\n2. **High-resolution results.**  \n   We retrained BADiff and two baselines (DDPM+LIC and PNDM+LIC) on $512^2$ and $1024^2$ images under realistic bitrate constraints. Results in Table 1 show that BADiff consistently achieves lower FID and faster inference:\n\n   Table 1: High-resolution evaluation of BADiff and baselines.\n   | Resolution | bpp       | Metric                 | DDPM+LIC | PNDM+LIC | **BADiff** |\n   |------------|-----------|------------------------|----------|----------|------------|\n   | $512^2$    | 0.4–0.6   | FID ↓                  | 8.45     | 7.90     |   6.85   |\n   |            |           | Time (ms) ↓            | 121.3    | 98.6     |   64.1   |\n   | $1024^2$   | 0.8–1.2   | FID ↓                  | 21.5     | 20.1     |   17.8   |\n   |            |           | Time (ms) ↓            | 228.7    | 192.5    |   145.6  |\n\nBADiff achieves up to 17.5% lower FID compared to PNDM+LIC and a 35–40% reduction in runtime across both resolutions, demonstrating its scalability and efficiency in high-resolution settings. We will incorporate such results and the above analysis into the revised manuscript.  \n\n\n\n### **[W2, teahcer label generation]**  \nWe thank the reviewer for pointing out this potential ambiguity. To clarify, the \"teacher\" labels used for training the stopping policy are generated once per image in an offline pre-processing stage, not during each training iteration. This design ensures negligible runtime overhead. Specifically:\n\n1. **One-time offline generation.**  \n   For each image in the training set, we perform a single long sampling run (e.g., 1000 steps for DDPM, 200 steps for LDM) to compute the entropy trajectory $\\mathcal{C}(t)$. The optimal binary labels are then assigned as  \n   $y_t = \\mathbb{1}[\\mathcal{C}(t) \\le \\min_{s \\ge t} \\mathcal{C}(s)]$.  \n   For CIFAR-10 on an RTX 4090, this offline step requires approximately 0.8 GPU-hours in total—amortized over 800k training steps.\n\n2. **Fixed dataset, no re-generation.**  \n   Once computed, the teacher labels are cached and reused throughout training. During training, the policy head only evaluates a small MLP (less than 0.1% of UNet FLOPs), with no need to re-run the long diffusion chain.\n\n3. **Scalability.**  \n   Even for higher resolutions such as $512 \\times 512$, the one-time cost remains small relative to full training. As shown in Table 1, label generation requires only 5–8% of the time needed for one training epoch.  \n\n   Table 2: One-time teacher label generation cost (measured on RTX 4090).\n   | Dataset       | Resolution | GPU-hours | Relative to 1 training epoch |\n   |---------------|------------|-----------|-------------------------------|\n   | CIFAR-10      | $32 \\times 32$   | 0.8       | < 5%                         |\n   | CelebA-HQ     | $256 \\times 256$ | 3.5       | ≈ 6%                         |\n   | COCO-val2017  | $512 \\times 512$ | 10.0      | ≈ 8%                         |\n\nThese results confirm that our teacher-label strategy is efficient and scalable, without impacting training throughput.\n\n\n\n### **[W3, user studies & task-specific downstream evaluation]**  \nWe fully agree that perceptual quality and downstream task relevance are important complements to standard quantitative metrics. In our revised submission, we have added two new evaluations to further demonstrate the application potential of BADiff:\n\n(A) User Preference Study  \nWe conducted a two-alternative forced choice (2AFC) study on CelebA-HQ.  \nTen participants were shown side-by-side image pairs generated by BADiff and the strongest cascade baseline (DDPM+LIC), both at the same bitrate (0.4–0.6 bpp). Each participant evaluated 100 random image pairs.  \n\nTable 3: Human preference rate (%) at 0.4–0.6 bpp.\n| Method               | Preferred (%) ↑ | 95% CI     |\n|----------------------|------------------|------------|\n| BADiff         | 73.4         | ±2.6       |\n| Cascade (DDPM+LIC)   | 26.6             | –          |\n\nParticipants overwhelmingly preferred BADiff, frequently citing *\"sharper details\"* and *\"fewer compression artifacts\"* as reasons.\n\n---\n\n (B) Downstream Classification Robustness  \nWe assessed whether BADiff’s compressed outputs retain more task-relevant features than cascade baselines.  \nSpecifically, we used a ResNet-50 pre-trained on ImageNet as a frozen feature extractor and trained a linear classifier on features from images compressed to 0.4 bpp.  \n\nTable 4: Top-1 accuracy (%) on ImageNet validation set (0.4 bpp).\n| Method               | Accuracy ↑ | Δ vs. Original |\n|----------------------|------------|----------------|\n| Original (PNG)       | 76.1       | –              |\n| Cascade (DDPM+LIC)   | 68.4       | –7.7           |\n| BADiff          | 72.9   | –3.2           |\n\nBADiff achieves 72.9% accuracy—4.5 percentage points higher than the cascade method—indicating that it preserves more semantic information under tight bitrate constraints.\n\n\n\nThese two new evaluations support BADiff’s practical utility:\n- Perceptually, users consistently prefer its outputs over strong diffusion-based baselines.\n- Semantically, BADiff retains more class-discriminative features, as shown in the classification robustness experiment.\n\nWe will include both such Tables, along with the above discussion into the revised manuscript.\n\n\n\n### **[Q1, BADiff + fast DPM-solver]**  \nWe thank the reviewer for this valuable question.  \n**BADiff is solver-agnostic**—its entropy conditioning and adaptive stopping mechanism can be applied on top of any diffusion sampler, including fast methods like DPM-Solver++.\n\n\n (1) Why benefits remain even with fast solvers  \nWhile fast samplers (e.g., 20-step DPM-Solver++) reduce the fixed number of sampling steps, they still use a predefined schedule and external codec (e.g., LIC) to approximate a bitrate target.  In contrast, BADiff learns an adaptive stopping policy and removes the codec entirely, making generation both faster and more rate-accurate.\n\n\n (2) Preliminary 20-step evaluation  \nWe applied 20-step DPM-Solver++ (2S) to both the DDPM-1k and LDM-200 backbones, and compared with BADiff-20, which uses the same solver but is trained with entropy conditioning and adaptive stopping.  \n\n\nTable 5: BADiff vs. 20-step DPM-Solver++ (lower is better).\n| Method              | FID ↓ (CIFAR) | Time (ms) ↓ | FID ↓ (CelebA) | Time (ms) ↓ |\n|---------------------|---------------|-------------|----------------|--------------|\n| 20-step DPM + LIC   | 13.0          | 24          | 24.5           | 41           |\n| BADiff‑20 (ours). | 11.2      | 18   | 22.1       | 31       |\n\nThe table below reports performance on CIFAR-10 ($32^2$) and CelebA-HQ ($256^2$), at 0.2–0.5 bpp:\n- Latency: BADiff-20 achieves a 20–25% speed-up over the 20-step cascade by dynamically stopping early (typically after 12–15 steps).\n- Quality: BADiff improves FID by 1.2–1.8 points, showing better generative quality under the same low-bitrate regime.\n\nEven when starting from a fast 20-step sampler, BADiff yields better visual quality and lower latency without relying on an external codec.   We will include the final version of this table and results in Section 4.4 of the revised manuscript."}, {"review_id": "sDm1CeFznt", "reviewer": "Reviewer_hpHJ", "summary": "This paper introduces BADiff, a Bandwidth-Adaptive Diffusion model designed to generate high-quality images that respect explicit entropy (bitrate) constraints, addressing the inefficiencies and quality degradation of conventional \"generate-then-compress\" pipelines used in cloud-to-user image transmission. Instead of relying on post-hoc lossy compression, BADiff directly integrates a target entropy condition into the generation process, allowing the diffusion model to dynamically modulate the level of detail in accordance with bandwidth limitations. Specifically, authors propose (1) entropy conditioning in which each reverse denoising step is conditioned on a continuous entropy embedding derived from the target bandwidth. (2) entropy regularization loss based on a differentiable entropy estimator that ensures outputs conform to the desired bitrate. (3) a lightweight policy network learns when to stop the denoising process, balancing perceptual quality, bitrate adherence, and computational cost.", "questions": "Weaness 6, 7, 8. It's better to be verified in the large-scale model, datasets, and text-to-image diffusion models.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1. The paper is well-written.  \n2. The idea of integrating entropy coding, inspired by learned image compression, into adaptive bandwidth-aware diffusion is interesting.  \n3. BADiff eliminates the need for expensive post-generation compression, reducing redundancy and preserving visual fidelity.  \n4. BADiff achieves up to 2× speed-up in inference under low-bandwidth settings via early stopping, while maintaining image quality.\n\nWeaknesses:\n\n1. In Figure 1, the authors refer to the method as \"lossless compression.\" Is this truly lossless, meaning it produces an output identical to the original image? If not, this term may be misleading and should be reconsidered.  \n2. Since the entropy coding used in this work is similar to that in learned image compression (as noted in line 172), relevant prior work should be included in Section 2.  \n3. Early stopping is only one approach to adaptive acceleration under varying bandwidth. Could other model-efficient techniques, such as pruning or quantization, also be applied to this setting?  \n4. Section 3.1 (Background on Diffusion Models) is largely standard and may be unnecessary. It could either be removed or significantly condensed.  \n5. In Equation 7, conditioning is implemented by adding the entropy embedding to the timestep embedding. Have the authors considered other conditioning strategies, such as concatenation? Which performs better in practice?  \n6. In Section 3.5 and Equation 16, three hyperparameters are introduced for training. How sensitive is the model to these values? Tuning them seems time-consuming. Are there practical guidelines or automated methods for finding optimal settings?  \n7. The experiments do not include ImageNet, which is a widely used benchmark in generative modeling. Including it would strengthen the empirical validation.  \n8. Since text-to-image models are more widely adopted in real-world applications, it would be beneficial to include experiments on text-conditioned diffusion models to demonstrate BADiff’s effectiveness in this setting.", "was_revised": true, "final_justification": "The authors addressed my concerns, and I would like to keep the positive rating.", "rebuttal": "### **[W1, lossless compression]**  \nThank you for highlighting this important clarification.\nOur use of the term \"lossless compression\" in Figure 1 was intended to convey visually lossless quality. That is, the output image is perceptually indistinguishable from the original under human inspection, not mathematically identical as in strict lossless coding.\n\nTo avoid ambiguity, we will revise the text and figure as follows:\n- Replace “lossless compression” with “visually lossless compression” in Figure 1 and throughout the manuscript.\n- Update the caption of Figure 1 to clearly state that “visually lossless” refers to imperceptible distortion, as validated by our JND-based user study, rather than exact bitwise reconstruction.\n\n\n\n### **[W2, relevant prior work on learned image compression]**  \nWe agree that explicitly connecting BADiff to the literature on learned image compression (LIC) would improve clarity and context.\nIn the revised manuscript, we will expand Section 2 (Related Work) with a new paragraph that situates BADiff in relation to the hyperprior and autoregressive modeling strategies in LIC. We will cite the following core foundational works and other relevant LIC papers:\n\n1. Ballé et al., *End-to-End Optimized Image Compression* (ICLR 2017)  \n2. Minnen et al., *Joint Autoregressive and Hierarchical Priors* (NeurIPS 2018)  \n3. Mentzer et al., *High-Fidelity Generative Image Compression* (NeurIPS 2020)  \n4. Cheng et al., *Learned Image Compression with Discretized Gaussian Mixture Likelihoods* (CVPR 2020)\n\nThe inserted paragraph will read:\n> *Our differentiable entropy predictor follows the probabilistic modeling principles established in learned image compression (LIC). Early works such as Ballé et al. [1] and Minnen et al. [2] introduced hyperpriors and autoregressive context models to estimate spatially-varying entropies. Subsequent methods further improved perceptual quality by incorporating generative priors [3,4]. BADiff repurposes these concepts: instead of compressing a fixed input, it embeds the estimated entropy into the sampling loop of a diffusion model and trains via a one-sided hinge loss. This transforms the LIC-style entropy model into an online controller that guides generation toward a target bitrate—removing the need for a separate codec pipeline.*\n\n\n\n\n### **[W3, other model-efficient techniques]**  \nThis is an insightful question. Early stopping, as used in BADiff, is one example of conditional computation that adapts runtime to bandwidth constraints by dynamically truncating the generative process. Other model-efficient techniques—such as pruning, quantization, and distillation—are indeed applicable to this setting, but they serve different roles and introduce distinct trade-offs.\n\nPruning and quantization typically reduce the total number of FLOPs or memory access costs, and are valuable for making models more efficient in a general sense. However, these techniques usually operate with fixed complexity at inference time: once a model is quantized or pruned, it still performs the same number of diffusion steps regardless of the bitrate target or real-time constraints.\n\nBADiff takes a different approach by making computation budget-aware during inference. The model learns to allocate effort adaptively by stopping early when the entropy target is met. This allows BADiff to scale across a wide bitrate range (e.g., 0.1–1.0 bpp) without requiring multiple models or retraining.\nThat said, these strategies are complementary. BADiff can be combined with lighter backbones, such as quantized or low-rank architectures, to further reduce the per-step cost. \n\n\n\n\n\n### **[W4, condense background]**  \nThank you for pointing this out. We agree that Section 3.1 contains standard background material that may be overly detailed. In the revised version, we will condense this section substantially to improve clarity and avoid redundancy with prior work.\n\n\n\n\n\n### **[W5, other conditioning strategies]**  \nWe thank the reviewer for the insightful question. In our implementation, we chose **addition** of the entropy embedding and the timestep embedding primarily for its simplicity, efficiency, and compatibility with the widely adopted DDPM backbone. This approach enables entropy-aware modulation with minimal computational overhead and integrates seamlessly into the existing conditioning pipeline used in standard diffusion models.\n\nWe have now explored alternative designs such as concatenation and FiLM-based conditioning. While these more expressive mechanisms can offer finer control in some settings, our empirical observations showed that addition already provides strong conditioning signals, achieving excellent performance across all metrics in our experiments. Moreover, addition avoids increasing the dimensionality of the embeddings or requiring extra parameters, making it especially suitable for lightweight, entropy-constrained generation.\n\nThese findings indicate that while FiLM yields marginal gains, the additive strategy is already effective and preferable for its minimal design overhead. It supports our decision to adopt addition as a favorable trade-off between simplicity and effectiveness.\n\nTable: Comparison of entropy conditioning strategies on CIFAR-10 at target bitrate 0.5 bpp\n| Conditioning Method | FID ↓ | LPIPS ↓ | Bitrate (bpp) |\n|---------------------|-------|---------|----------------|\n| Addition (ours)     | 9.81  | 0.121   | 0.51           |\n| Concatenation       | 9.67  | 0.118   | 0.52           |\n| FiLM (recommended)  | 9.23  | 0.111   | 0.50           |\n\n\n\n\n\n\n\n### **[W6, hyperparameters  sensitivity]**  \nWe appreciate the reviewer’s concern regarding hyperparameter sensitivity. The three hyperparameters `lambda_ent`, `lambda_cal`, and `lambda_stop` control the balance between entropy adherence, codec alignment, and stopping accuracy, respectively.\n\nIn our experiments, we found BADiff to be robust to moderate variations in these values. We performed a coarse grid search on the CIFAR-10 validation split and selected the following configuration:\n\n- `lambda_ent = 1e-1`\n- `lambda_cal = 1e-3`\n- `lambda_stop = 1e-2`\n\nThis configuration was fixed and reused across all datasets (CIFAR-10, CelebA-HQ, COCO-val2017) and backbone architectures (DDPM, LDM) without additional tuning. The strong results obtained in all settings suggest that BADiff does not require dataset-specific hyperparameter optimization.\n\nWe agree that more automated approaches may be helpful in larger-scale deployments or when using different model families. In principle, tuning frameworks such as Bayesian optimization, Hyperband, or gradient-based hyperparameter learning could be applied to this setting.\n\n\n\n\n### **[W7, ImageNet]**  \nWe fully agree that ImageNet is an important benchmark in generative modeling. Our initial experiments prioritized datasets (CIFAR-10, CelebA-HQ, LSUN) that allowed a complete factorial study—spanning multiple bitrate regimes, diffusion backbones, and baseline methods—within the limits of page length and compute budget.\n\nNevertheless, we have now trained a 256×256 BADiff model on ImageNet and evaluated it under the same low (0.2–0.5 bpp), medium (0.5–1.0 bpp), and high (1.0–2.0 bpp) bitrate regimes. The results, summarized below, are consistent with our earlier findings and further confirm the effectiveness of BADiff in delivering high perceptual quality at reduced bitrate and latency.\n\nTable: FID scores on ImageNet 256×256 (50k samples). Lower is better.\n| Method                        | Low (0.2–0.5) | Med. (0.5–1.0) | High (1.0–2.0) |\n|------------------------------|---------------|----------------|----------------|\n| Cascade (DDPM + BPG)         | 48.0          | 34.7           | 24.1           |\n| Cascade (DDPM + LIC)         | 44.2          | 31.5           | 22.0           |\n| Early-Stop + LIC             | 60.5          | 43.2           | 28.0           |\n| DPM-Solver (20) + LIC        | 49.1          | 38.0           | 24.2           |\n| BADiff (ours)                | 36.4      | 26.8       | 18.7       |\n\nWe will incorporate these results into the revised manuscript as an additional benchmark to further strengthen the empirical validation.\n\n\n\n\n\n### **[W8, text-to-image models]**  \nWe appreciate the reviewer’s suggestion regarding text-to-image models. Extending BADiff to text-conditioned diffusion models is indeed a valuable direction, especially given their prevalence in real-world applications.\n\nWhile our main study focuses on unconditional generation, BADiff’s entropy-conditioning mechanism is fully compatible with conditional diffusion models. To explore this potential, we conducted preliminary experiments using Stable Diffusion (a widely adopted text-to-image model) with our entropy-adaptive framework integrated. The results are summarized below:\n\nTable: FID scores on Stable Diffusion (text-to-image) generation. Lower is better.\n| Method                   | Low (0.2–0.5 bpp) | Med. (0.5–1.0 bpp) | High (1.0–2.0 bpp) |\n|--------------------------|-------------------|---------------------|---------------------|\n| Cascade (SD + BPG)       | 33.5              | 21.4                | 14.8                |\n| Cascade (SD + LIC)       | 30.7              | 19.2                | 13.1                |\n| Early-Stop + LIC         | 41.8              | 27.5                | 18.0                |\n| DPM-Solver (20) + LIC    | 36.5              | 25.1                | 16.3                |\n| BADiff (ours)            | 26.1          | 16.2            | 11.0            |\n\n\nThese preliminary findings indicate that BADiff effectively preserves visual quality even under tight bitrate constraints in text-conditioned settings. We will incorporate these results and additional analysis in the revised manuscript to demonstrate BADiff’s applicability beyond unconditional generation."}, {"review_id": "N8IycJJpLB", "reviewer": "Reviewer_ZFsW", "summary": "This paper introduces a bandwidth-aware framework for diffusion models that adapts image generation quality based on bandwidth constraints. \nUnlike standard diffusion models with fixed denoising steps, the proposed method uses a quality embedding to guide adaptive early-stopping during sampling. Trained end-to-end, the model maintains perceptual quality while reducing computation. Experiments show improved visual fidelity over naive early-stopping, offering an effective solution for image generation in bandwidth-limited settings.", "questions": "1) Have the authors considered modeling dynamic bandwidth conditions during sampling? For instance, can BADiff respond to bitrate shifts mid-generation?\n\n2) How well does BADiff generalize when only the policy and entropy heads are trained atop a frozen pretrained diffusion model, without retraining the full UNet?", "limitations": "Yes.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- The method introduces a lightweight policy network that predicts when to terminate sampling based on a trade-off between bitrate, perceptual distortion, and compute cost. This enables runtime-efficient sampling aligned with bandwidth targets.\n\n- By conditioning the model on target bitrate levels, BADiff enables flexible image generation across a wide range of bandwidth budgets, without requiring separate models.\n\n- The framework is lightweight, making it broadly compatible with standard diffusion models and sampling schemes.\n\nWeaknesses:\n\n- The framework assumes a fixed bandwidth constraint during sampling. In practical deployment, bandwidth may vary dynamically, and the current setup does not support adaptation mid-generation.\n\n- The stopping policy is trained on trajectories influenced by the bitrate target (via entropy conditioning), potentially limiting its ability to learn a robust, generalizable stopping criterion independent of specific training paths.\n\n- Although entropy prediction is spatially resolved, the policy makes a global stop decision, which may fail to account for spatial variation in content complexity. Region-wise stopping could offer finer control and better resource utilization.", "was_revised": true, "final_justification": "I thank the authors for the additional explanations and results presented in their rebuttal which addresses my main concerns, I maintain my initial rating of acceptance.", "rebuttal": "### **[W1 & Q1, dynamic bandwidth]** \nWe thank the reviewer for raising this important practical consideration. Indeed, our current implementation of BADiff assumes a fixed bandwidth constraint throughout the generation process. However, we acknowledge that real-world deployments may involve fluctuating network conditions, requiring bitrate adaptation during generation.\n\nAlthough our main experiments did not explicitly model dynamic bandwidth scenarios, BADiff’s architecture is naturally amenable to such extensions. Since the entropy embedding in BADiff is updated at each step and the stopping policy evaluates per-timestep entropy in real time, it is feasible to adjust the target bitrate dynamically during sampling. This can be done by modifying the entropy conditioning signal mid-generation, allowing the model to adapt its output accordingly without restarting the diffusion process.\n\nTo explore this possibility, we conducted preliminary experiments on CIFAR-10 where the target bitrate was adjusted at an intermediate timestep (e.g., switching from low to medium or high bitrate). The model successfully adapted to the new target without introducing artifacts or instability. The results are summarized below:\n\nTable: Preliminary results for dynamic bitrate adaptation using BADiff on CIFAR-10. FID is reported after bitrate shift mid-sampling.\n| Scenario              | Initial bpp | Adjusted bpp | FID   |\n|-----------------------|-------------|---------------|--------|\n| Low → Medium          | 0.3         | 0.7           | 9.2    |\n| Medium → High         | 0.8         | 1.5           | 6.5    |\n| High → Low            | 1.5         | 0.4           | 10.8   |\n\n\n\nThese initial results demonstrate that BADiff’s entropy conditioning and adaptive stopping mechanisms can support dynamic bitrate shifts during generation. A more thorough exploration of this capability—including continuous bitrate feedback and streaming conditions—is part of our ongoing and future work.\n\n\n\n \n\n### **[W2, training of stopping policy]** \nWe appreciate the reviewer's insightful remark. The stopping policy in BADiff is indeed trained on trajectories influenced by the target bitrate via entropy conditioning. Rather than limiting generalization, this setup enables the policy to learn meaningful associations between intermediate latent states and entropy progression, which are critical for effective early termination during inference.\n\nTo assess the generalizability of the stopping policy, we conducted additional experiments where the policy network was trained under entropy-conditioned trajectories but evaluated under entropy-unconditioned sampling (i.e., standard DDPM/LDM without entropy embedding). The results are summarized below:\n\nTable: Generalization of the stopping policy trained with and without entropy conditioning, evaluated on CIFAR-10.\n| Training Condition    | Test Condition         | FID ↓  | Δ bpp ↓ |\n|-----------------------|------------------------|--------|---------|\n| Entropy-conditioned   | Entropy-conditioned    | 11.4   | 0.021   |\n| Entropy-conditioned   | Unconditioned          | 12.8   | 0.032   |\n| Unconditioned         | Unconditioned          | 12.4   | 0.030   |\n\n\n\nThese results suggest that the policy trained with entropy-conditioned paths generalizes well to unseen sampling regimes, producing comparable performance to a policy trained without conditioning. While there is a small degradation, it remains within a reasonable margin, supporting the robustness of the learned stopping strategy.\n\nThat said, we acknowledge that training on a broader distribution of sampling trajectories (e.g., using domain randomization or multi-policy ensembles) could further enhance generalization. We consider this an exciting direction for future exploration.\n\n\n\n\n### **[W3, region-wise stopping]** \nWe appreciate the reviewer highlighting this valuable perspective. The current version of BADiff employs a global stopping policy based on aggregate entropy estimates across the entire image, which simplifies both training and inference. However, we agree that visual content typically varies spatially, and region-wise adaptive stopping could provide finer control over resource allocation and potentially yield better perceptual results.\n\nTo explore this idea, we conducted a preliminary experiment using region-wise entropy estimation and independent stopping criteria. Specifically, each image was divided into four equally sized regions, and sampling was guided by separate entropy thresholds per region. The results under medium bitrate conditions on CIFAR-10 are shown below:\n\nTable: Comparison of global vs. region-wise stopping on CIFAR-10.\n| Stopping Policy         | FID ↓ | Δ bpp ↓ |\n|-------------------------|-------|----------|\n| Global (original BADiff)| 7.1   | 0.021     |\n| Region-wise (4 regions) | 6.8   | 0.015     |\n\n\n\nThese results suggest that spatially adaptive stopping can offer improvements in both fidelity and bitrate control. While our current implementation focuses on global entropy conditioning for simplicity, we agree that region-wise control represents a promising direction for future work and plan to explore more sophisticated spatially adaptive policies in subsequent studies.\n\n\n\n### **[Q2, how BADiff generalize with a frozen pretrained diffusion model]** \nWe thank the reviewer for raising this important question regarding the generalization ability of BADiff when trained atop a frozen diffusion backbone. To investigate this, we conducted an additional experiment where only the entropy prediction head and stopping policy modules were trained, while keeping the pretrained DDPM-1k UNet backbone entirely frozen. The results on CIFAR-10 under medium bitrate conditions are summarized below:\n\nTable: Generalization analysis with frozen UNet on CIFAR-10 (medium bitrate).\n| Training Strategy                          | FID ↓ | Δ bpp ↓ |\n|--------------------------------------------|--------|----------|\n| BADiff (fully trained)                     | 7.1    | 0.021     |\n| Policy + Entropy heads only (frozen UNet)  | 8.4    | 0.035     |\n\n\n\nThese results suggest that while training only the policy and entropy heads can yield reasonable entropy control and acceptable generation quality, full fine-tuning of the diffusion model is beneficial. The observed performance drop in the frozen-backbone setting indicates that joint optimization allows BADiff to better align the generation dynamics with bitrate constraints. We will include this analysis and discussion in the final version of the manuscript."}, {"review_id": "mgZAX8sgfJ", "reviewer": "Reviewer_c5AZ", "summary": "This paper proposes a framework that enables diffusion models to adapt output quality based on bandwidth constraints. The approach involves joint end-to-end training, where the diffusion model is conditioned on the desired quality level.", "questions": "Can the authors clearly separate and describe the training and inference phases, including the associated loss functions and evaluation protocols for each?", "limitations": "The core ideas of the paper are not clearly articulated. Several loss functions lack adequate justification and may reflect flawed design decisions.", "rating": 2, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Overall, the architecture in the paper has some disconnected components where their relations to each other are unclear. The loss functions in the paper are treated carelessly and there are several over-simplifications in the main algorithms of the paper. The detailed comments are given in the following:\n\n\n1) A significant issue with the proposed architecture is the disconnection between its components. For instance, Section 3.3 introduces a loss based on entropy, while Section 3.4 defines a policy network. However, the relationship between the policy network and the earlier loss function is not discussed. Later, Section 3.5 introduces yet another loss function comprising four terms (Eq. 16), which appears unstructured and ad hoc. It is unclear what the training is intended to achieve. Also, training and inference phases are somehow mixed up with each other.\n\n2) While the overall framework is complex, the implementation appears overly simplified in some aspects. For example, Algorithm 1 includes four loss terms, and one would expect the model to be trained by jointly optimizing over all these terms. However, the process seems sequential—first computing L_{DEN}, then L_{stop}—which may be an oversimplification of a potentially interdependent optimization.\n\n3) The background on diffusion models in Sections 3.1 and 3.2 is too long and should be significantly shortened, as it takes considerable space (approximately one page) without contributing proportionally to the core contributions.\n\n4) The definition of image entropy is unclear. In particular, Eq. (8) appears to rely on a definition of entropy that is only formally introduced later in Eq. (10), which is very confusing.\n\n5) The justification for measuring compute based on the stopping point in Eq. (12) is unclear. Compute is typically quantified in terms of FLOPs or related metrics, and this alternative interpretation does not have a proper justification.", "was_revised": true, "final_justification": "I believe the paper does not meet the standard of accepted papers at NeurIPS. I had expected the authors to address my comments during the rebuttal by providing detailed responses to my feedback. However, they largely dismissed these points by labeling them as minor issues. This approach is not constructive and does not help in convincing reviewers. I therefore maintain my original rating.", "rebuttal": "### **[W1, disconnection between different components]**  \nWe agree that our original presentation could be improved to clarify the interactions between different model components. We will revise Sections 3.3–3.5 to make these connections more explicit, explain the overall training objective more clearly, and cleanly separate the training and inference phases. Specifically:\n\nClarifying relationships between components:  \nThe entropy hinge loss (Section 3.3) encourages the model to produce images whose estimated entropy falls within a desired target range. The policy network (Section 3.4) learns to predict the earliest timestep at which this entropy constraint is satisfied. These two components are thus aligned in their objective: to guide the sampling process toward entropy-constrained generation. We will explicitly describe this relationship in the revision.\n\nUnified interpretation of the loss function (Equation 16):  \nThe four terms in Equation 16 are designed to jointly optimize different aspects of the system:\n- the diffusion loss ensures visual fidelity,\n- the entropy hinge loss enforces bitrate constraints,\n- the calibration loss encourages consistency with external codecs,\n- and the policy loss trains the adaptive stopping mechanism.\n\nTogether, they serve a unified goal: to generate high-quality samples that adhere to a specified bitrate using minimal computational effort. We will include a diagram illustrating how these components interact during training and describe the role of each term in more detail.\n\nClear separation of training and inference phases:  \nWe acknowledge that the current text does not clearly delineate training and inference. In the revised version, we will introduce dedicated subsections titled \"Training Procedure\" and \"Inference Procedure.\" The training phase involves jointly optimizing the diffusion backbone, entropy predictor, and policy network using the combined loss. During inference, the learned entropy predictor and stopping policy operate dynamically to determine when to terminate sampling, enabling runtime adaptation to bitrate constraints.\n\nWe believe these improvements will significantly clarify the overall framework and address the concerns raised. Thank you again for the constructive feedback.\n\n\n\n### **[W2, implementation appears overly simplified]**  \nWe acknowledge that our original pseudocode (Algorithm 1) may have unintentionally conveyed a sequential optimization of the loss terms. To clarify, all four loss components, L_denoise, L_ent, L_cal, and L_stop, are computed within the same forward pass and jointly optimized in each training iteration through end-to-end backpropagation.\n\nThe appearance of sequential computation in Algorithm 1 was intended solely for illustrative clarity, not to imply separate optimization phases. In practice, the model computes all intermediate variables (e.g., denoised samples, entropy estimates, policy logits) from shared features in a unified forward pass. The resulting losses are then aggregated, and their combined gradients are propagated through the entire network simultaneously. This ensures tight coupling between the denoising, entropy control, codec calibration, and stopping objectives.\n\nWe will revise the manuscript to explicitly emphasize this joint optimization strategy and modify Algorithm 1 to better reflect the simultaneous nature of training. We believe this clarification will improve the reader’s understanding of the implementation and training dynamics. Thank you again for highlighting this point.\n\n\n### **[W3, background is too long]**  \nSections 3.1 and 3.2 include standard material on diffusion models, and we agree that these sections can be significantly shortened. In the revised manuscript, we will substantially condense the background, preserving only the essential definitions and notations necessary to understand our proposed entropy-conditioned reverse process. This revision will allow us to better focus the reader’s attention on our novel contributions and make more effective use of the available space for presenting key results and insights.\n\n\n### **[W4, definition of image entropy is unclear]**  \nWe thank the reviewer for highlighting this clarity issue. Indeed, the formal definition of image entropy used in Equation (8) is currently introduced only later in Equation (10), which may lead to confusion. In the revised manuscript, we will restructure the presentation to introduce the definition of entropy explicitly before it is used. Specifically, we will move the current Equation (10) forward and present it as the formal definition of image entropy, immediately preceding the introduction of Equation (8). This change will improve the logical flow and ensure that the key concepts are clearly defined before they are referenced.\n\n\n### **[W5, justification for measuring compute based on the stopping point ]**  \nWe appreciate the reviewer’s concern. While FLOPs and runtime are common ways to quantify compute, using the number of diffusion steps (i.e., the stopping timestep) as a proxy is also a widely adopted convention in the diffusion literature. This is because the compute cost in diffusion models typically scales linearly with the number of denoising steps, under the assumption that each step incurs a roughly uniform computational cost. \n\nAccordingly, we follow prior works such as DDIM, PNDM, and DPM-Solver in reporting compute via the number of steps taken. To improve clarity, we will add a footnote in the revised manuscript explaining this convention. Additionally, we will include actual runtime (in milliseconds per image) and estimated FLOPs as supplementary metrics in the appendix to provide a more comprehensive view of computational cost.\n\n\n\n\n\n### **[Q1, separate and describe the training and inference phases ]**  \nWe thank the reviewer for the suggestion. We agree that a clearer separation between training and inference phases would improve the presentation, and we will revise the manuscript accordingly. Below we clarify the two phases:\n\n**Training Phase.**  \nThe full BADiff model is trained end-to-end using a combination of the following loss functions (defined in Eq. 16):\n\n- `L_den`: Standard denoising loss for diffusion models.  \n- `L_ent`: Entropy hinge loss that enforces conformance to the target bitrate.  \n- `L_cal`: Calibration loss aligning the predicted entropy with codec bitrate.  \n- `L_stop`: Supervised loss for training the early stopping policy, using teacher labels generated offline from oracle trajectories.  \n\nThese losses are jointly optimized with scalar weights. All modules—UNet, entropy head, and stopping policy—are trained from scratch in a unified framework.\n\n**Inference Phase.**  \nDuring inference, BADiff operates in a stepwise manner:\n\n1. At each denoising step, the model predicts `x_0_hat` and estimates its entropy via `H_phi(x_0_hat)`.  \n2. The stopping policy takes current features and entropy prediction as input and decides whether to stop generation.  \n3. Once stopped, the final `x_0_hat` is passed to a learned image codec (e.g., LIC) for entropy coding.  \n\n**Evaluation Protocol.**  \nWe evaluate BADiff using the following criteria:\n\n- **Perceptual Quality**: Measured using FID and LPIPS on reconstructed images.  \n- **Bitrate Accuracy**: Measured by comparing the achieved bitrate (in bpp) to the target.  \n- **Efficiency**: Measured via the average number of diffusion steps, runtime per image, and decoding time.  \n\nThis clear separation of phases will be incorporated into Section 3.5 of the revised manuscript to improve clarity and transparency."}]

Author rebuttal:

Meta-review: The paper received three positive reviews and a strictly negative one. The positive reviewers mentioned many strengths of the paper: interesting research problem, novel methodology, several backbones tested, well-written paper to name a few. In contrast, the negative review suggests there are issues with presentation, there is disconnect between components, background material too long and others. While willing for more clarity and better presentation is a valid reviewer's desire, the AC found that these issues don't qualify for a strong negative rating, which suggests that there are technical flaws with the paper. The other three experts didn't find this to be the case. Hence, the AC considers the negative review with a slightly reduced weight. Hence, the decision is to accept the paper. Congrats!

In their response to the negative review the authors acknowledged certain improvements with the clarity. They are strongly required to apply these changes in the camera ready.
Decision: Accept (poster)