Improving Progressive Generation with Decomposable Flow Matching
Authors: Moayed Haji-Ali
Willi Menapace
Ivan Skorokhodov
Arpit Sahni
Sergey Tulyakov
Vicente Ordonez
Aliaksandr Siarohin
Venue: NeurIPS 2025 poster ()
Keywords: Image generation
video generation
diffusion models
Primary area: deep_learning

Abstract: Generating high-dimensional visual modalities is a computationally intensive task. A common solution is progressive generation, where the outputs are synthesized in a coarse-to-fine spectral autoregressive manner. While diffusion models benefit from the coarse-to-fine nature of denoising, explicit multi-stage architectures are rarely adopted. These architectures have increased the complexity of the overall approach, introducing the need for a custom diffusion formulation, decomposition-dependent stage transitions, ad-hoc samplers, or a model cascade. Our contribution, Decomposable Flow Matching (DFM), is a simple and effective framework for the progressive generation of visual media. DFM applies Flow Matching independently at each level of a user-defined multi-scale representation (such as Laplacian pyramid). As shown by our experiments, our approach improves visual quality for both images and videos, featuring superior results compared to prior multistage frameworks. On Imagenet-1k 512px, DFM achieves 35.2% improvements in Frechet DINOv2 Distance (FDD) scores over the base architecture and 26.4% over the best-performing baseline, under the same training compute. When applied to finetuning of large models, such as FLUX, DFM shows faster convergence speed to the training distribution. Crucially, all these advantages are achieved with a single model, architectural simplicity, and minimal modifications to existing training pipelines.

Improving Progressive Generation with Decomposable Flow Matching
Moayed Haji-Ali
Willi Menapace
Ivan Skorokhodoy²
Arpit Sahni?
Sergey Tulyakov
Vicente Ordonez!
Aliaksandr Siarohin
Rice University
Snap Inc
Project Webpage: http::/ssup--essuuud.iiibbbbbbbb
Abstract
Generating nigh-dimensional visual modalities is computationally intensive task. A common solution progressive generation, where the outputs are synthesized in a coarse-to-fine spectral autoregressive manner. While diffusion models benefit from the coarse-to-fine nature of denoising, explicit multi-stage architectures are rarely adopted. These architectures have increased the complexity of the overall approach, introducing the need for custom diffusion formulation, decomposition- dependent stage transitions, ad-hoc samplers, Decomposable Flow Matching (DFM), is a simple and effective framework for the progressive generation of visual media. DFM applies Flow Matching indepen- dently at each level of a defr-nd multi-scale representation (such as Laplacian pyramid). As shown by experiments, approach improves visual quality for both images and videos, featuring superior results compared to prior multi- stage frameworks. On Imagenet- 1k 512px, DFM achieves 35.2% improvements in Frechet DINOv2 Distance (FDD) scores over the base architecture and 26.4% over the best-performing baseline, under the finetuning of large models, such as FLUX, DFM shows faster convergence speed to the training distribution. Crucially, all these advantages are achieved with single model, architectural simplicity, and minimal modifications to existing training pipelines.
model cascade. Our contribution,
training compute. When applied
Introduction
The high dimensionality of images and videos poses a challenge for generative modeling. An approach to make the problem more tractable involves decomposing the generative task into sequence of simpler sub-problems. An increasing number of generative models adopt this practice by
progressively modeling visual signals of increasing resolution [1] 16,
18]
41 [2]. Autoregressive
generative models, for instance, have demonstrated that switching from a next-token prediction
next-scale [42] or frequency [66 prediction pattern, yields substantial performance improvements. Recently, the success of diffusion models has been connected form of spectral autoregression enforced by the diffusion process which erases details progressively from the coarsest to the finest
pattern in ID sequence of flattened tokens [4] 6 24 35
49 50
[30 36 38
'Equal Contribution.
Work partially done during an internship at Snap Inc.
39th Conference on Neural Information Processing Systems (NeurIPS 2025),

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Flow Matching
Pyramidal Flow
renoise
Coscaded Modeling
per stago
Framework
70
cond.
Ap:: Models Count
Figure 1: Comparison of different diffusion frameworks. Cascaded models employ a separate model per stage. Pyramidal Flow [18] progressively increases resolution through careful upsampling and renoising operations. Our framework models multiple stages independently from each other within the same model, enabling progressive generation with minimal modifications to Flow Matching [27]
have reformulated the diffusion process to enforce spectral autoregression, an approach we refer to as progressive modeling. This is typically realized by restructuring the diffusion process to include transition points where the signal resolution altered, thereby defining a sequence of stages of progressively increasing resolution. Key progressive
variety of diffusion frameworks [
18
modeling paradigms are illustrated in Figure]] [ where cascaded models [13 14 37 and Pyramidal
Flow [8] are exemplified and contrasted with vanilla Flow Matching [26 27 However, while
these frameworks demonstrate the feasibility the progressive paradigm, they often operate directly in pixel space [ 41]. depend multiple models [13
14 37 41,, deviate from the original formulation of the diffusion process [1 9 18 41] Such deviations introduce complexities in managing inter-stage transitions, requiring careful consideration of operations such resizing [T I8 41), renoising [ 18 41 or blurring 41 and, in some instances, require specialized samplers 9
To address these challenges, we propose Decomposable Flow Matching (DFM), progressive modeling framework based on a simple extension of Flow Matching, depicted in Figure 2 At its core, user-defined decomposition function is applied to the input, producing multiscale input representation that defines each stage of the generation, and Flow Matching process is independently applied to each stage, utilizing set of per-stage flow timesteps. During inference, standard sampler operates separately on each stage of the representation guided by a user-defined sampler schedule that dictates the progression of flow timesteps per each stage. Timesteps evolved sequentially, starting from the coarsest stage; progression to a subsequent stage only begins once the preceding stage has reached predefined threshold. During training, progressive generation is simulated by selecting a stage, sampling a noise level for it, and injecting the maximal noise level into subsequent stages of the representation and small noise level to preceding without the need for expert models, ad-hoc diffusion processes, or specialized samplers, all while offering the flexibility of user-defined input decomposition.
These capabilities realized
We conduct thorough analysis the design space for DFM, providing insights into its behavior across different training and sampling strategies, and model architectures. Based these findings, instantiate DFM and evaluate its performance on established image and video generation benchmarks, specifically ImageNet- 1K [5] and Kinetics-700 [3]. Our results demonstrate uniform improvements over Flow Matching (27). cascaded models, and Pyramidal Flow [1]]. Furthermore, we apply DFM to the finetuning of FLUX 23 demonstrating its efficacy in enhancing the performance of large-scale generative models. Compared with standard full finetuning, applying DFM for the same amount of finetuning iterations yields 29.7% reduction in FID and 3.7% increase in CLIP score.
In summary, our work introduces Decomposable Flow Matching, a novel progressive generation framework that offers several key advantages: (i) It presents simple formulation rooted in Flow Matching; (ii) is agnostic to the choice of decompositions; (iii) it does not need multiple models per-stage training; (iv) it includes comprehensive analysis of critical training and sampling hyperparameters; (v) it outperforms existing ofate-of-thh-ar progressive generation frameworks on ImageNet-IK IK [5] and Kinetics-700 [3], and enhances FLUX 23 finetuning performance.
2 Related Work
2.1 Progressive Generation in Autoregressive Models
Autoregressive models for visual generation 4
formulate the generation of visual data as a next-token prediction problem. This is typically achieved by first obtaining a
24
31
35
49
50

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Algorithm Sampling procedure of training timesteps across multi-scale stages
1: procedure SAMPLETRAININGGTIISTTTSSSS
Input: S
total number of scales
Output: (t'....,
2: Q < SAMPPLEDSSCEEEDDSTRUUUTOOOO
stage index corresponding to #scales
3: t SAMPLELOOGINORMMA/Y 0)
4: for = to Q do
5:
SAMPLELOGGNNONNAL(m 1.5) end for
6:
7:
for Q+ + S do
8:
ta + 0 end for
9:
10: return (t'....,t5) {5)
end procedure
discrete input representation, which is then flattened into a 1D sequence to enable autoregressive modeling. However, recent work [16 42 has demonstrated that flattening undermines the intrinsic multidimensional structure of visual data. VAR [42] addresses this limitation by modeling image generation as a spectral autoregressive process. A multiscale tokenizer generates discrete tokens at different resolutions, and the model predicts each scale conditioned on the previous ones, yielding substantial improvements over baselines. NFIG [T6] adopts similar approach where frequency decomposition is used to define different scales that predicted autoregressively. In work, explore spectral autoregression in the context of diffusion models.
2.2 Progressive Generation in Diffusion Models
Diffusion models have achieved state-of-the-ar results across various visual generation tasks 7 2
28 46 Their effectiveness has been linked implicit form of spectral autoregression, whereby the diffusion process erases fine-grained details a coarse-to- fashion 30 36 38).
Several progressive generation frameworks made spectral autoregression explicit part of their design, generating their outputs stage-by-stage. Cascaded diffusion models [13 14 generate low-resolution outputs in an initial stage, followed by upsampling stages conditioned on previous outputs. separate model used for each stage. Other methods redefine the generative process to incorporate progressive signal transformations. f-DM [9] and RDM [41] introduce stages via downsampling, MDM [10] simultancously denoises multiple resolutions. Edify Image [ introduces frequency-speciffe attenuation in the diffusion process. Pyramidal Flow Matching [18] operates in the latent space over a hierarchy of increasing resolutions, combining upsampling and re-noising operations. Despite these advances, existing approaches share limitations. They often require complex stage-transition mechanisms [1
or tailored samplers g 41. are tightly coupled to specific and primarily focus pixel-space generation [1 io 41] In contrast, we propose a simple and generic framework for progressive generation in the latent space that supports user-defined decompositions without altering the core architecture.
9
decomposition strategies [1
9 8
2.3 Autoencoders with Spectral Latent Structure
Coarse-to-fine or spectral autoregressive modeling benefits from an autoencoder with a well- structured spectral representation where low-, mid-, and high-frequency components in the RGB space correspond the respective low-, mid-, and high-frequency components in the latent rep- resentation. Modern image and video autoencoders typically lack such spectral structure (38), so recent works fine-tune them enforce the desired spectral properties through scale equivariance regularization [17 22 38). Another viable strategy is to train Spectral Image Tokenizer [8] like model from scratch, which encodes a wavelet-decomposed image representation into a causally ordered sequence, yielding spectrally structured latents by design. Our framework is agnostic to the choice of the autoencoder benefits from such spectral latent structure, and we opt for the first strategy of fine-tuning with scale equivariance 22 38 to stay closer to existing diffusion pipelines.

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Sampling Schedule
Timestep Sampling 29
P
M
Soop
P
Rec.
Dec.
H
DiT
X
Previews
DiT
D2
X
DiT
2
X
X
Solver
(a) Inference
(b) Training
(c) Architecture
Figure 2: Overview of Decomposable Flow Matching (a) Sampling procedure. A sampling schedule defined that dictates the timestep progression of each stage. The model predicts velocities for each input scale and vanilla sampler denoises each scale according to its schedule. Intermediate stages can decoded during inference to provide low-resolution preview of the generation. (b) Training procedure. A stage index sampled from a discrete probability distribution and defines the main stage. Timesteps for each stage are sampled accordingly. The model minimizes velocity prediction errors for each scale. (c) DiT [33] architecture for progressive generation. Patchification layers and time embedders are replicated for each scale.
Method
This section details our progressive generation framework, summarized in Figure 2 The method is based on Flow Matching 226 27). which is introduced in Section 3.1 A Laplacian decomposition strategy, detailed in Section 3.2 is exemplified
way of producing multiscale input representation amenable to stage-by-stage progressive modeling. In Section 3.3 the Flow Matching framework extended account for the multiple stages by introducing per-stage flow timesteps, which are leveraged to instantiate the progressive generation scheme by denoising stages one-by-one, starting from the coarsest. Finally, the DIT 33 architecture is extended in Section 3.4 support the proposed generation scheme by introducing per-scale patchification and time embedding layers.
3.1 Flow Matching
We base our generative models the Flow Matching framework 26
which defines generation of data X, Pa as the progressive transformation of X₂ following path comnecting samples from the two distributions. Often, the path instantiated as a linear interpolation: X, fX; + (1 t X)X and Xo ax. given by dt X1 Xu- A generator G is trained to predict this velocity by minimizing:
NO,, (I) originates from noise distribution (27]. The velocity along this path is
C X Xom-p G( - well
where pr a training-time distribution over f. At inference, samples are generated from noise using an ODE solver (e.g.. Euler), integrating the learned velocity field to produce data samples.
3.2 Input Representations for Progressive Modeling
The high dimensionality visual modalities makes their modeling challenging. This complexity can be reduced by factorizing their generation into simpler stages. instantiating a progressive generation framework which generates coarse details such as structure first, and finer details later.
To this end, each input X is structured into multiscale representation P ) across S scales, each defining a generative stage, containing a progressively increasing level of detail, from the most coarse to the finest. Various decomposition techniques are viable, including DWT, DCT, Fourier transforms, or multiscale autoencoders (8). We adopt the Laplacian pyramid due its simplicity and flexibility, but note that, unlike existing methods, our framework is agnostic to the particular choice of decomposition. The pyramid levels are defined as:
4

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X down X, s) up(down(X, 1), if s=
(2)
down X,
where each scale is associated with user-defined resolution, and down(..., and up( ... 8) respectively represent downsampling and upsampling to the resolution s. A downsampled approxi- mation of the input can be obtained as X X X
3.3 Decomposable Flow Matching
The multiscale input is amenable to progressive modeling. We define a number of stages where each stage models set of scales from the coarsest to the finest. We extend Flow Matching support multistage generation. To this end, we introduce an independent flow timesteps 1 for each scale, and formulate the forward process as:
P Pr....,es (X where X = t'x + (1-
(3)
The factorization of flow timesteps enables control over stage generation by imposing conditional generation previous stages and marginalization successive stages by respectively applying low or full noise levels [2]. To this end, we define a discrete distribution Py over the number sampling stages, and for each scale within the sampled stage Q, draw timesteps independently from predefined logit-normal distribution Pi.Q. Consequently, rather than predicting a single velocity, the model predicts per-scale velocities v² using shared generator G conditioned the full set of noisy input scales and their timesteps, which is learned by minimizing:
E Eq e qum Ximpa, No Σ M || (Pa,..,s t th....,t (8 v² -..,,,t))") (4)
where Pg represents the discrete distribution over the number of stages, Q represents the sampled stage, Pt represents the training distribution of each scale timesteps, and G. represents the the model velocity prediction for scale
During inference, a timestep schedule is defined that activates stages progressively as shown in Figure 2a The sampler starts from the first stage and advances 1 only, before introducing subsequent scales one at a time once the last introduced scale reaches a predefined threshold r in its generation. Then, the last stage along with all previous stages, continues the generation at different rates (see Sampling Schedule in Figure 2 (a)). Each time the generated scale reaches its threshold, the representation can undergo partial decoding up the current stage, producing an output preview. At the end of the generation, all scales representations are summed to visualize the generated output.
Both the stage distribution Py and the training timestep distribution Pt central effective learning of this progressive strategy, and training timesteps are chosen to simulate the progressive sampling through stages, shown in Figure 2b) First, stage index, representing the number of stages that are currently under generation, is sampled from a discrete probability distribution Py- Given the stage number, sample the timestep of the last scale within the stage according to a logit normal distribution [7]. For every preceding stage, we instead sample the respective timestep from a logit normal distribution shifted towards lower noise levels to simulate inference time behavior where the earlier stages are less noisy than the last stage currently being generated. For simplicity, we apply the same shift to all preceding scales, using the same logit-normal parameters across them. Finally, the timesteps for each subsequent stage are set to zero to prevent the model from spending its capacity in modeling such zeroed scales. Algorithm! [ shows the procedure for sampling the stage index and the timesteps for each scale within the stage. We additionally introduce a masking term M that ignores their loss contributions. This promotes progressive learning dynamics, where the model focuses on global structure before local detail, enabling high-quality progressive generation.
3.4
Architectural Adaptations
We choose to experiment on DiT architecture [K due to the pervasive adoption of its variants 7 48). and we extend it to accommodate multiscale inputs and their associated flow
2
25
28
46
5

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Table 1: Ablation results on Imagenet- IK [5] using DiT-B backbone.
Res. FiD
FD 4 IS
Res.
FlD
FDD 1S
Res.
FiD1ox & FDDrox
15
(o) Fize stage somp, prnks y2
Tej Arehtteecerrr
(e) Compute Allocation
D.7
512
36.02
6760
32.2
baseline
512
29.56
571.0 (
41.0
Butch size Patch
512
31,95
615.0
39.9
088
512
$2.09
-masking
581.0
40.0
29.56
571.0
0.9
512
29.56
571.0
41.0
-landandizaatio
512
27.13
505.0
42.8
(0 Inpur Decompottion
0.95
512
27.5
540.0
43.7
(d) Porumeter Specialication
512 1024
1024
58.03
899.0
20.3
(b)
Previoss snale Ingworm Jocation
Nome
28.37
564.0
41.5
256-552--11
1024
1024
40.60
683.2
318
0.0
512
29.83
567.0
40.4
Mod.
512
28.95
568.0
41A
256 > 10044
1024
41.06
704.0
30.9
0.5
512
28.89
569.0
41:5
Proj.
512
29.56
571.0
41.0
29.14
567.0
Cond.
565.0
40.0
1.5
512
29.56
371.0
41.0
Amn.
28.99
564.0
40.7
2.0
512
29.96
589.0
39.8
MLP
512
27.65
$45.0
43.0
Tidd
512
885.0
Full
512
26.63
$26.0
45.5
timesteps (see Figure 2 At their core, DiT transforms the input visual modality into a sequence of tokens through linear layer called patchification layer, where each token corresponds to a small portion of the input of size k x k, denoted as patch size. An inverse operation is performed by the output patchification layer. sequence of transformer blocks [45] processes the token sequence. To make the model aware of the input timestep, a limestep embedder MLP produces respective conditioning embedding, which is passed to the transformer blocks through modulation layers.
To accommodate multiscale inputs, rather than using single input and output patchification layers, dedicated input and output patchification layers are instantiated per scale. Patch sizes are chosen such that each input scale yields an equal number of patches, ensuring consistent spatial alignment across scales. For example, for two stages of resolution 256 x 256 and 512 x 512, we use patch sizes of 1 x 1 and 2 x 2, respectively. The resulting patch embeddings from all scales are summed and fed into the transformer backbone. Finally, a dedicated per-scar per-scale projection layer used to output each scale velocity. Loss masks M are integrated to zero out model inputs at masked scales. This prevents noisy inputs whose contribution to the loss negated by the mask from harming model performance. To incorporate the per-scale timesteps, we use dedicated timestep embedder for each level and sum their outputs to form unified conditioning signal.
Experiments
4.1 Experimental setup
Latent space The FLUX (23 and Cogvideo [48] autoencoders are used, respectively, to produce the latent spaces for all image and video experiments. To maximize the benefits of coarse-to- fine modeling, low-, mid-, and high-frequency components in the latents should correspond to the respective low-, mid-, and high-frequency RGB components once decoded, a property not typically found modern autoencoders. We establish it for all autoencoders by scale-equivariant finetuning (38. Namely, we fine-tune the FLUX autoencoder for 10,000 steps our internal image dataset at 2ess-reso with x2-4 scale equivariance regularization
38 with a batch size of 64.
Training details We train our models on the ImageNet-IK IK [5] and Kinetics-700 [ datasets. We run all ablations using DiT-B and main experiments on the DiT-XL architecture. All experiments use batch size of 256, learning rate of 1e-4 with 10k steps warmup, gradient clipping of 1.0, the Adam [2I] optimizer, and an EMA with 8 = 0.9999. We train ablations on ImageNet- IK for 600k steps, and the main experiment for 500k and 350k steps, respectively, for 512px and 1024px resolution. For Kinetics- 700, we train the main experiments for 200k steps.
Evaluation metrics and protocol We report FID, and Inception Score (IS) for image experiments and frame-FII FID and FVD 43 for video experiments. We also include FDD (Frechet Distance computed against DINOv2 use 50k generated samples for ImageNet- K 512px evaluation and 10k samples for the rest of the experiments. We report main experiment results with cfg [22 values of 1.0, 1.25, and 1.5 as (3)
32 features) as it was shown to be more reliable metric than FID [20] 39]. We
4.2 Training Parameters Ablation
We conduct ablations to provide insights into the behavior of the main training hyperparameter. Unless otherwise specified, the ablations are run on ImageNet-1K. 1K (3) 512px using a DíT-B backbone. The default backbone employs a 2-stage Laplacian decomposition of 256px and 512px resolution,

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608
8:14
11.05
6.31
2384
6.31
20
15
10
31.8
35.8
12:24
25:32
14:14
14:53
20
10
15
2014
1843
2:08
2031
2534
16:44
28.23
14:15
FID
003
25
20
36.89
23:22
22.03
13:11
12:0
15
25
20
1233
1224
2-8
14.03
15.44
10-
20
35
30
11.34
12:33
12:35
10
3
35
30
1564
1018
1331
40
25.15
11.27
14.35
40
1665
21.8
18.23
18.22
15
20
20
steps
(a) ImageNet-1K (5) 512px
(b) ImageNet- IK
1024px
Figure 3: FOD results ablating sampling configuration, threshold, and per-stage steps.
Table 2: DFM efficiency comparison with Flow Matching
Model
# Params
Peak Memory
GFLOPs
Forward Lateney
Train Iter Speed Sampling Time
Flow Matching
712.
6.258 GB
524.613
60.25 ms
297.39 ms
2.43 s
DFM
716.482 M
6.294 GB
524.638
61.32 ms
301.00 ms
2.43 s
respectively, where each decomposed input scale is normalized to unit standard deviation. Results are presented in Table 1 and practical guidance on their optimal configuration is provided in
Appendix Sec. A.5
Training timestep distribution. The sampling distribution of timesteps pr during training is crucial as it determines the implicit loss weighting for each stage (see Section 3.3) We parametrize its design across two dimensions. The first is the distribution over the stage index s, which corresponds to a number of scales being trained. Since we ablate over 2-stage configuration, this can be expressed as the probability of sampling stage 0 (p)). The second is the location for the logit normal distribution 7 of all preceding stages, representing the amount of bias towards lower noise levels for generrted stages. We report the performance of various sampling strategies in Table [ (a) and (b). Performance positively impacted by large probabilities of sampling stage O, indicating that allocating more model capacity towards predicting structural details benefits generation. This is aligned with previous cascaded model training strategies, where the first stage model is trained longer than the second stage model [29]. Performance is also positively impacted by larger shifts in the logit normal distribution of simulates the inference- time sampling schedule. We found that location values of 0.5, 1.0, and 1.5 yield comparable performance, with differences of less than 1 %% in FDD and 1.3% in IS. A larger location value, however, simulates availability of a cleaner first scale (low-fre now-frequency) result and aligns more closely to inference time behavior. We hypothesize that under the increased DiT/XL capacity used in the main experiments, a closer alignment to inference-ting behavior would be beneficial as we speculate that larger models may afford spending more capacity for non-structural details. Therefore, we select 2e = 0.9 and location of 1.5 for our main experiments. Finally, we consider strategy that ties the timesteps of every stage, enforcing the same value for them, and accordingly modify sampling. This variation presents degraded performance loses the benefits of progressive generation.
scales through previous stages, as this better
Architecture. We ablate our baseline by removing input masking (see Section 3.4p and removing the normalization of each stage to unit standard deviation before the application of the diffusion process. We report the results in (c). Removing input masking for successive stages degrades performance over all metrics due to the negative influence of injecting pure noise tensors into the model. However, we found that removing standardization improves performance. Removing normalization results in lower magnitude for the input of the second stage. This affects the model in similar way to increasing pg giving more importance to stage 1 structural modeling and improving performance. Therefore, we adopt masking but exclude standardization for our main experiment.
Parameter Specialization. We leverage the factorization of generation into multiple stages by exploring model parameter specialization for each stage. Specifically, in addition to base model parameters, we create set of per-stage model parameters acting stage experts, akin to using distinct sets of model parameters cascaded models. During the generation of stage s, the specialized version of the weights corresponding to is averaged with the base model parameter, enabling scale- specific behavior without significant computational overhead. As shown in Table specialization improves performance when applied to MLP layers and produces the best results when applied to every model parameter. Despite its performance benefit, we exclude this technique from our main experiments to keep the parameter count similar across baselines.
parameter

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Table Comparison baselines on ImageNet- 1K [5] and Kinetics-700 [ using a DiT-XL model
and training convergence plot for ImageNet- IK [5] 512px.
ImageNet 512
ImageNer 102
Kineries 512pr
1000
FiDauk
FDDbox 4
FiDuu.
FDDjox 4 IS
FID.o. 1 FDD
FVD.ox
200
Canclana
Fiim Metth
Flow Matching
15.89
282.9
58.5
42.18
575.9
26.7
12.6
370.1
304.1
Cct
Cascaded
13.67
260.9
72.7
20.16
318.3
55.0
13.81
346.2
317.2
Pyramidal
10.98
261.2
77.3
16.9
351.1
64.0
10.51
353.8
265.6
DFM (Ours)
9.77
200.6
77.9
14.11
277.3
78.2
9.98
336.7
260.2
Hlow Matching (efge1.225)
7:59
185.7
31.57
405.3
39.4
10.1
312.9
297.0
400
Cascuded (cfg-1122)) 1,25)
6.80
163.0
11.68
221.9
89.2
11,62
279.9
Pyramidal Flow (cfg=1.225)
4,95
164.7
132.0
9.38
245.7
109.3
8.24
292.2
266.3 3
DFM (Ours) (efg==1.25)
4.28
120.0
135.6
7.56
181.7
130.2
7.88
277.5
257.4
Flow Mutching (cfg=1.55
4.73
132.5
138.9
24.68
412.5
46.0
8.43
263.4
309.8
Pyramidal Flow (.5)
Cascaded (cfg-1.5)
4.57
5.68
114.0
116.2
191.0
118.1
7.68
8.23
185.9
167.3
152.5
126.8
10.39
6.98
247.1
235.0
327.1
280.2
200
105k
300k 50ck
DFM (Ouns) (e5g=11.5)
4.28
85.8
196.8
6.42
6.85
236.5
271.7
Training Steps
Compute allocation. Compared with single-stage model, input decomposition entails lower dimensionality for earlier stages which results in saved computation at similar settings. In the abla- tions, for example, the first stage corresponds to 256px inputs rather than 512px. Such computational savings can be leveraged by either increasing the training batch size and number of inference steps reducing the DiT patch size so that each stage results in equal number of tokens. We observe performance increases at steady rate when reducing patch size, yet increasing the batch size quickly reaches a plateau, converging to lower performance as reported in Table (e). We select the patch size reduction strategy for the final model.
Input Decomposition. Our framework is agnostic the exact choice of input decomposition, and thus different number of stages or different resolutions at different stages can be seemingly applied. We explore different configurations of the Laplacian decomposition for 1024px ImageNet- generations and report the results in Table [
(f). Each decomposition is denoted as the sequence of resolutions corresponding to each stage e-g- 256-+1024 for 2-stage decomposition with 4x downsampling between stages. The 512- 1024 decomposition yields the worst performance due to the initial stage being performed in 5 12px resolution and containing larger amount of non-structural components, reducing the effectiveness of the progressive framework. We find the three-stage setting (256-512-+1022 to yield the best result. However, we adopt 2-stage decompositions of 256-+512 and 256-+1024 respectively, for 51 512px and 1024px experiments for easier comparison with baselines.
4.3 Sampling Parameters Ablation
This section analyzes the effects of sampling parameters on DiT-XI trained on ImageNet-1k 1 512px and 1024px using the optimal training parameters discussed Section 4.2 Results are given in Figure and practical guidance on their optimal configuration is provided the Appendix Sec. A.5
Stage Timestep Thresholds. We analyze the optimal timestep threshold r determining the switch between sampling stages. We choose threshold of 0.7 for 512px as it produces the best FDD and second-best FID at the respective optimal cfg level and 0.95 for 1024px experiments.
Per-Stage Sampling Steps. We evaluate model performance using different numbers of steps allocated to the sampling of the first and second stages under sampling threshold of 0.7 and 0.95 respectively for 512px and 1024px. Allocating a larger number of steps to the first stage gives overall better performance, matching the intuition that the generation of structural details represents a more crucial component of sample quality than fine-gma fine-grained details. We fix total number of steps equal to 40 for our experiments and choose 30 and 10 sampling steps, respectively, for the two stages.
4.4 Comparison to baselines
Baselines selection and details. We select baselines corresponding to the main generation paradigms in Figure [[] which we train on the same underlying model backbone, ensuring a constant amount of training compute. The cascaded model baseline consists of separate models, one for each stage. Two stages are employed to avoid excessive error accumulation. We train the first stage model for 80% of the total training iterations and use it to initialize the second stage model for faster convergence. Pyramidal Flow [8] is chosen due to its state-of-the-art progressive generation performance and due to it operating in latent spaces while using rectified flow formulation. We operate it in a 2 and 3-stage configuration for 512px and 1024px datasets, ensuring the same base resolution across

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(Ouns)
Masching
Cascaded
Pyramidal Flow
(Quns)
Marching
Cascaded
Pyramiaal Flow
Figure 4: Comparison of DFM against baselines ImageNet- 1K 512px [5] selected samples.
Samples are generated with cfg 3.0
experiments. All baselines are configured ensure the same amount of training compute. Please refer to Appendix Sec. B for exact details on each baseline.
Results. As shown in Table our method surpasses the baselines across all metrics and efg settings with the exception of Kinetics- 3 FDD. Notably, DFM matches baselines best reported FDD in roughly half of the number of iterations, while using the same training compute (See Figure 4 right) Qualitative comparison (see Figure 4 and Appendix Sec. [ suggests that DFM generates better structural details, an observation which we attribute its progressive formulation which focuses the model's 's capacity on its lowest resolution stage.
Efficiency. To ensure fair comparison, keep the training compute budget comparable across all baselines in Table We further benchmark DFM against Flow Matching in Table on DiT-XL. As shown, the additional patchification and timestep-embeddingg layers introduced by DFM incur only a minor increase in parameters and training FLOPS, translating to less than 1 1.2% slowdown per training iteration.
4.5 Finetuning of large-scale models
To evaluate the effectiveness DFM in large-scale generative models, we finetune FLUX-dev (23) our internal image dataset using DFM and scale equivari- autoencoder. First, the original FLUX model is finetuned for 24k steps to adapt to the scale equiv- ariant autoencoder. Starting from this checkpoint, branch two finetunings. The first continues regular fine- tuning obtain the FLUX-FT checkpoint, the second finetunes for our framework to obtain the FLUX-DFM checkpoint. Both finetuned for 32k steps under the same settings and training compute. We use FLUX-dev patchification and projection layers weights to initialize the first stage layers of FLUX-DFM, and zero-initalize the second stage layers. We train on multiple aspect ratios and use total batchsize of 192 for the 1024px resolution. More details on the finetuning are included in the
Table 4: FLUX fine-tuning comparison.
Method
FID 4 FDD 4
CLIPSIM f
FLUX FLUX-FT
17.79
172.7
0.3280
12.56
153.6
0.3261
FLUX-DFM
8.83
116.2
0.3381
Appendix Sec. B We compare the baselines by generating 10k samples from validation split of our internal dataset and report FID, FDD, and CLIP (4) similarity (CLIPSIM) in Table 4 We include qualitative results and comparisons for FLUX-DFI DFM Figure and Appendix Sec. FLUX-DDF achieves consistently better performance compared with standard full finetuning. improving FID and FDD by 78.7% and 24.3%, respectively. We report original FLUX-dev checkpoint numbers as a reference. Please note that in this experiment, we do not aim to improve FL.UX-dev quality but rather show that finetuning with DFM achieves overall faster convergence in learning the finetuning dataset distribution. Thus, report FID and FDD reliable metrics comparing FLUX-FT and FLUX-DFN,

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OOPS
FLUX-FT
FLUX-DEM
FLUX-FT
FLUX-DEM
FLUX-FT
FLUX-DFM
Figure 5: (Top) Qualitative results produced by FLUX 23 finetuned with DFM. (Bottom) a compar- ison of FLUX-DFM the baseline (FLUX-FT).
5 Discussion
Limitations Similarly to other progressive generation frameworks [1 18 41 our method introduces additional training and sampling hyperparameters. The framework's most important hyperparameters balance between learning of low and high-frequency visual components, enabling users to pose more emphasis on structural details. When excessive importance is put on structural details, a decreased presence of high-freque freeueeecuncy details is noticed. We provide extensive ablations, and practical guidance for their setup, and show that the same parameters can be reused across different settings. We provide further ablations and guidance in Appendix Sec. Sec.[Aland discuss further our framework limitations and failed experiments in Appendix Sec. and Appendix Sec. G
Conclusions We propose DFM, novel framework for the progressive generation of images and videos. Differently from existing formulations, our framework is simple, agnostic the choice of decompositions and does not necessitate multiple networks. We analyze it to provide insights into its main training and sampling hyperparameters and show that outperforms both Flow Matching and the wate-of-the-an progressive diffusion formulations on both ImageNet- K [5] and Kinetics- 700 [3] We further validate the effectiveness of DFM on large-scale models, showing its faster convergence than standard full fine-tuning. A promising avenue for future work is to explore other decomposition paradigms such as discrete cosine, wavelet transforms, and multiscale autoencoders. Extending these findings to large-scale settings remains an exciting direction for future research.
Acknowledgments The authors thank Anil Kag and Dishani Lahiri for their engineering support.

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Appendix
Appendix Contents
Framework Details
14
A.1
DFM Implementation Details
14
A.2
DFM Training Details
14
A.3
DFM Dataset Details
15
A
4
Inference Details
15
A.5
Choosing Training and Inference Hyperparameter
15
Baseline Details.
15
Additional Evaluation Results and Details
16
Autoencoders without Scale Equivariance
17
Large Scale Finetuning
18
E.1 FLUX DFM Finetuning
18
Failed Experiments
18
Limitations
19
Framework Details
A.1 DEM Implementation Details
We base architecture modified version of DIT 33
Specifically, we normalize the data across scales by applying scale-wise pre- and postconditioning following the scheme of [19], which ensures that each input and output distribution has unit variance in expectation. Additionally, replace VIT frequency-based positional embeddings applied in DiT [33] with 2D rotary positional embeddings (RoPE) 40 due its wide adaptation recent models
Furthermore, we 25 46).
condition the model on the stage being generated by adding an embedding of the current stage index the modulation signal. Finally, we drop the class label conditioning 10% of the time enable classifier-free guidance.
To adapt the DIT 33 for video generation, patchify the latent frames independently and apply tokenwise concatenation of the resulting tokens [46]. Furthermore, we replace the 2D RoPE with 3D) RoPE adapt the position information to the video input. Finally, our ablations Kinetics-700 reveal that unlike the FLUX autoencoder (See Table. (c)). Cogvideo latents benefit from standardizing the input to have unit variance before the application of the diffusion process. Therefore, we apply such standardization to all of our video experiments.
A.2 DFM Training Details
=-10- 10-8) and base learning rate of 0.0001 with 10k linear warmup steps, weight decay of 0.01, and total batchsize of 256. The main experiments are trained with DiT-XL/2 on ImageNet-1K K for 512px and 1024px, respectively, for 500k and 350k steps. the main video experiments on Kinetics-700, we train for 200k steps. Ablations trained with DiT-B/2 for 600k steps using the same hyperparameters the main experiments.
We train using the Adam optimizer (31 0.9, B2 = 0.99, c=
14

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ImageNet-1K IK 512px experiments are trained on a single node containing 8 H100 GPUs, whereas ImageNet-1K 1K 1024px and Kinetics-700 512px experiments used nodes of the same type. Ablations were trained on single node.
A.3 DFM Dataset Details
Our main image experiments trained and evaluated on ImageNet-1K 1K (5) which has research-only, non-commercial license. Our video experiments are trained and evaluated on Kinetics-700 [3) which is available under the Creative Commons Attribution 4.0 (CC BY 4.0) license.
A.4 Inference Details
For all of our experiments, unless otherwise specified, we use an Euler ODE sampler with steps and linear timestep scheduler.
A.5 Choosing Training and Inference Hyperparameter
DFM introduces several training and inference hyperparameters. In practice, a default configuration of such hyperparameters generalizes well across different datasets and settings. In the following, we discuss such optimal configurations and summarize the observed effects of varying the main hyperparameters.
Using 2 stages works well for most experiments, where the first stage has resolution of 256px, while the second stage has resolution equal to the final resolution (see Table. 1). We find that a base resolution of 256px for the first stage contains an ideal amount of structural detail to support generation of the successive ones while not containing excessive amounts of fine-grained details.
Number of generation stages:
First stage sampling probability p.: We find that 0.9 generalizes well across different model sizes. The probability deternines the amount of model capacity spent on structural detail modeling, smaller models may benefit from higher values (see Table. 1)
Stage noise sampling parameters: At training time, we use logit normal distribution with parameter (location=O,, scale=1.0) for the stage currently sampled for training, and (location=1.5, scale=1.0) .00 for the previous stage. Larger location values for previous stages allow the model to leverage more structural details as conditioning during second stage generation, but expose the model more to train-inference mismatches if the first stage results are not generated with sufficient quality. Thus, larger location values are beneficial for larger models (see Table. 1).
Sampling stage threshold 0.9 generalizes well across different settings (see Figure 6)) As the parameter determines the amount of information in the first stage that the second stage can leverage as conditioning, in the presence of a high-quality first stage prediction, larger thresholds are desirable. While the optimal value varies depending on cfg, model, and dataset, find the suggested value to be reliable default.
Input standardization: Before applying noise, we standardize each level in the decomposed input representation to have unit-variance for Kinetics-700 video experiments using the Cog Video autoencoder, while this behavior disabled for ImageNet- image generation experiments with the FLUUX autoencoder. Standardization has impact loss magnitude for each stage, thus it acts similarly to the first stage sampling probability pf in balancing the amount of model capacity allocated to modeling structural details fine details. We found that the optimal parameters can vary depending on the autoencoder representation and suggest ablating over this setting when adopting new autoencoder.
B Baseline Details.
This section, includes details about the baselines training and inference. First, the base architecture described, then specific details about the Cascaded and Pyramidal Flow baselines are detailed.
15

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Table DFM with original (orig) and eeaveeequivariant (SE) FLUX autoencoder. Experiments are performed on DiT-B and trained on ImageNet- 1K [5] 512px for 400k steps.
Method
5lDsox +
FDDsox +
IS f
Flow Matching accoiiac-
54.50
855.5
21.4
DFM (FLUX-ac oc-or)))
34.00
630.1
34.2
Flow Matching (FLUX-ae-SEE)
43.16
728.85
26.6
DFM (FLUX-ac-SE)
32.89
626.5
35.0
Table 6: Comparison of various decomposition methods on ImageNet- IK different with different guidance (CFG) values are reported.
[5] 512px. Resutls at
CFG 1.0
CFG 1.25
CFG 1.5
FIDsok + FDDsox 4 IS 1
FIDsox 4 FDDsak
IS
FIDsok + FDDsok 4
IS 1
Flow Matching
15.89
282.9
58.5
7.59
185.7
97.2
4.73
132.5
138.9
Ours (DWT)
9.48
195.6
78.8
4.20
117.3
136.9
4.40
84.8
199.2
Ours (DCT)
9.60
194.4
78.6
4.19
115.1
138.3
4.37
82.5
201.2
Ours (Laplacian)
9.77
200.6
77.9
4.28
120.0
135.6
4.28
85.8
196.8
Baselines architecture. All baselines use the hyperparameters and architecture of [33], with the mod- ification to incorporate rotary positional embeddings (RoPE) [40] and Network Precondtioning [19] Inference performed with 40 steps using an Fuler sampler and a linear sampling schedule.
Cascaded baseline. We initially train the stage model following the spatial baseline for x 80% of the total training steps. To match the training and inference compute of the other baselines, we adopt a patch size of 1 x 1, yielding the same number of tokens as the other baselines. Subsequently, we finetune the stage model to obtain the stage 2 model, which upsamples the first stage output. For the stage 2 model, we introduce a dedicated pacification layer for the conditioning input from stage and concatenate its output tokens with those stage 2. We add a small amount of noise the conditioning input during training to reduce exposure bias. The amount of noise is sampled from logit normal distribution with scale parameters of 1.0 and location of 1 1.5. For inference, we perform grid search over the best inference parameters and found that equally dividing the inference steps between stage and stage (i. e. inference steps for each stage) and using noise level of 0.025 yields the best results. Therefore, we use these settings for evaluations.
Pyramidal Flow baseline. We follow Jin et al [8] in training the Pyramidal Flow baseline. For the three-stages experiments, we allocate twice the batch size for the second stage compared with the first and second stage following [1] and use gamma parameter of 0.33. In the two-stages experiments, we allocate an equal batch size between the first and second stages. During inference, we use an equal number of inference stapes for each stage.
C Additional Evaluation Results and Details
Choice of decomposition method. DFM employs multi-scale spatial representation that explicitly separates low- and high-frequency content. This separation can be realized with several decom- position methods(e.g.. Laplacian pyramid, discrete cosine transform (DCT), or discrete wavelet transform (DWT)) by decoding low- and high-frequency components independently. Despite their representational differences, we find the practical guidance on choosing the hyper-parameters in section A.5 still applies. We retrained DFM on ImageNet-I1 at 512px with DCT- and DWT-bbsedd decompositions using exactly the settings in Table 3 and report results in ??. As shown, using identical parae-eass yields comparable gains over the Toow-Macchin baseline across all decompositions, indicating that DFM is agnostic to the choice of decomposition and that the default parame-arsmeters are broadly transferable.
Sampling parameters ablation We report quantitative results ablating the role of different sampling hyperparameters in Figure and show qualitative results in Figure and Figure 19 ablating, respec- tively, sampling steps allocated to each stage, and different cfg and sampling threshold configurations. Increasing the number of steps allocated to the first stage results in improved image structure, while
16

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8.14
11.05
6.31
2384
6.31
2.13
20
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10
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14:53
20
10
15
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1843
2:08
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16:44
28.23
14:15
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25
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30
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11.34
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40
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35
228
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(a) ImageNet- IK [5) 512px
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1024px
Figure 6: FID FDD 10k and IS ablating sampling configuration, threshold, and per-stage steps on DiT-XL/2 trained with DFM on ImageNet-IK [5)
increasing the number of steps allocated to the second stage results in reduced gains which are ob- servable in areas with complex textures such as foliage, grass, animal fur. The sampling threshold has a reduced impact on generation quality and is most visible low cfg values.
Comparison to baselines Convergence behavior for DFM and baselines is shown in Figure 8 Figure 9 and Figure TO respectively, for ImageNet- IK [5] 512px, ImageNet-I (5) 1024px, and Kinetics- 700 [3. In addition, we show qualitative comparison on non-curated samples for DFM against baselines on ImageNet-I1K [5] 512px (see Figure ImageNet- (5) 1024px (see Figure
and Kinetics-700 [3] (see Figure
13 Figure 14 and Figure 15
Addtional qualitative results and
videos are provided in the Wehxite.
FLUX-DFM qualitative comparison with FLUX-FT. We provide additional qualitative comparison FLUX finetuned with DFM (FLUX-DFM) against FLUX with standard finetuning applied (FLUX-
FT) on 1024px text-to-image generation in Figure [6]and Figure [7
Qualitative results. We provide qualitative results ImageNet-IK IK (5] 512px of selected classes in
Figure 20
Figure 21 and Figure 22 Addtionally, we provide fully uncurated samples in Figure 23
Figure
24 and Figure 25
D Autoencoders without Scale Equivariance
DFM explicitly decouples low- and high-frequency content into two successive stages. The first stage diffuses coarse, low-frequency information. Its output then conditions the generation of high- frequency details in the second stage. Recent work shows that diffusion models follow this spectral autoregressive pattern implicitly [30 36 38 and proposed scale-equivariant autoencoders to improve this separation, making the produced latents easier to diffuse [38]. Although DFM is agnostic to the choice of autoencoder, we conduct our experiments with the autoencoders of (38) finetuned for seale equivariance to ensure desirable spectral properties both for baselines and DFM.
In this section, we explore the behavior of DFM on non-regularized autoencoders. Table reports comparison between Flow Matching and DFM on the original FLUX autoencoder and scale- equivariant FL.UX autoencoder for DřT-B architecture trained for 400k steps on ImageNet-1 [5). When the scale-cquivariant FLUX autoencoder is replaced with the original variant, Flow Matching
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suffers substantial drop in performance, whereas DFM preserves similar performance, thanks to its explicit spectral decomposition. both cases, DFM outperforms Flow Matching.
E
Large Scale Finetuning
This section explores the usage of DFM for fine-tuning large-scale models. Since the stage 1 input resembles a low-resolution version of the original input, we aim to preserve the pretrained model's behavior much possible. DFM adds per-stage patchification layer, timestep embedding, and output head, Accordingly, we reuse the pretrained patchification layer and timestep embedding for stage 1, while zero-initialising the corresponding stage modules. Before training, the framework therefore replicates the pretrained model's low-resolution predictions. After training, all weights (including patchification layers) are adapted to generate consistent stage 1 and stage outputs. To adjust the model patchfication layers weight to stage 1, which uses a smaller patch size, we upsample stage input by a factor of 2 before adding noise, halving the effective patch size. We then downsample the model's output to match stage resolution.
E.1 FLUX DFM Finetuning
We choose to fine-tune FLUX-DEV (23] due to its strong performance. To avoid biases introduced by cfg distillation, the distillation-guii sittionnggudnnee factor fixed at 1.0 throughout training, and all fine-tuning is carried internal dataset. We follow [38] to regularize the the FLUX autoencoder, yielding
eulvee-uuvaaian autoencoder.
Then, we perform cull-finetuning of FLUX for 24k steps to adjust it to the new autoencoder, producing FLUXXSE. During the initial training steps, we freeze all layers except the patchfication layers. Then, we finetune FLUX-SE for 32k steps to obtain FLUX-DFM. As baseline, we finetune FL.UX- SE for the same 32k steps using standard full-finetuning. Finetuning uses 1024-px and 512-px images at variable aspect ratios. We use Adam optimizer (31 0.9, 8 0.99, = 10 and base learning rate of 0.00001 with 2k linear warmup steps, weight decay of 0.01, and total batch size of 192. We drop the text conditioning 10% of the time to enable classifier-free guidance.
Please note that since FLUX-DEV is distilled and post-trained on highly aesthetic images, its distribution differs from that of our internal data. Therefore, a direct comparison with the original FLUX-DEV would not be informative. Rather, we measure speed in learning the new training distribution with DFM compared with standard full-finetuning at an equal training cost.
Inference. We evaluate using test split of 10k prompts from internal dataset. We 40 sampling steps and Euler ODE solver, cfg of 3.0, and distillation guidance factor of 1.0 (equivalent not applying efg).
F
Failed Experiments
DCT-Space DFM We apply DFM in the DCT space, where the input visual modality is represented in the frequency domain rather than the spatial domain. We obtain the DCT decomposition by first dividing the visual input into 2D or 3D blocks of pixels of size 4 or 8 and applying DCT to each of them. Different stages are formulated as the progressive modeling of DCT components of increased frequency. We find, however, that DiT models provide reduced performance when working in the frequency rather than the spatial domain, a finding we speculate may originate from an increased difficulty of leveraging token similarities in attention operations. While experiments showed that DCT can be used as a way of producing the input decomposition. input to the DiT model should be converted to the spatial domain for optimal performance, and the Laplacian decomposition is preferred due to its simplicity.
Alternative parameter specialization methods As parameter specialization showed the capabil- ity of increasing the model's performance (see Table. (d)), we investigate alternative ways of specializing model parameters per each stage. As an alternative avenue, we investigate the recent Tokenformer (47 architecture due to its capacity to progressively integrate new parameters during training. In particular, we instantiate shared set of parameters and set of specialized parameters for each stage. The shared set of parameters is always active, while the specialized parameters activated only when corresponding to the currently active stage. We find the Tokenformer [47]
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5
Sampling Steps Stage
Figure 7: (left) Selected samples highlighting failure cases generated by our framework trained on ImageNet-1K [5] 512px on DiT-XL for 1.3M iterations. When generating high-frequenu details such as fine structures, vegetation or cluttered environments, DFM may produce artifacts. (right) Artifacts can be mitigated by increasing the number of sampling steps for the second stage.
architecture to underperform the regular DiT design when given the same amount of computation, thus we abort this experiment. To reduce the number of parameters required for specialization. we wrap each linear layer in different LoRA wrappers [15] 44), one for each stage, and activate the respective wrapper when the corresponding stage selected training or inference. LoRA showed improved results over the baseline when utilizing high LoRA ranks which resulted in similar parameter counts full parameter specialization.
Expert Models We train separate or expert models for each stage rather than a joint model. We then evaluate performance by mixing expert models trained for different numbers of steps. We find that performance improves steadily with more training of the first stage and improves marginally with more training with longer training of the second stage model, supporting the intuition that modeling of structural detail has larger importance to sample quality. To reduce the computational burden of training separate models for each stage, we explore finetuning the second stage model starting from the first stage model with positive results. Despite positive results, the idea is not explored further due the increased complexity of maintaining separate models for each stage. We note that, in principle, it is possible to obtain expert models by finetuning jointly trained model separately for each stage with full LoRA finetuning. We leave the exploration of this possibility as future work.
G Limitations
DFM improves modeling visual inputs by decomposing them into different components. The framework's 's hyperparameters control the amount of model capacity dedicated to modeling each of the components. As an example, a larger probability of sampling stage 0 (pf) during training (see Table. (a)) results in larger emphasis on structural details. As shown in Figure 7 selected samples containing large amounts of high- sighufreyeency components such as vegetation, fur. thin structures, or cluttered environments may exhibit artifacts in such regions which manifest as a flattened appearance. Increasing the number of sampling steps for the second stage (see Figure 7 (right) and Figure (8) mitigates such artifacts. By acting training sampling probabilities for each stage, and distribution of sampling steps between different stages, the framework allows for balance between structural and fine details modeling quality.
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1000
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Figure 8: Convergence curves for different datasets and metrics comparing our framework to baselines on ImageNet- 1K [ 512px.
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Figure 10: Convergence curves for different datasets and metrics comparing our framework to baselines on Kinetics-700 3 512px.
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DFM (Ours)
Masching
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Quaats het S
Figure II: Comparison DFM against baselines on DiT-XL trained on ImageNet- IK 512px S for
500k steps. Samples are fully uncurated and generated with cfg 3.0.
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DFM (Ours)
Masching
Cascaded
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Matching
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Figure 12: Comparison of DFM against baselines on DiT-XL trained on ImageNet- 1024px [5] for
350k steps. Samples are fully uncurated and generated with cfg 3.0.
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DOP Sourt
Figure 13: Comparison of DFM against baselines DiT-XL trained Kinetics-700 [3] 512px for
200k steps. Samples are fully uncurated and generated with cfg 3.0.
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the wasth
Figure 14: Comparison of DFM against baselines DiT-XL trained Kinetics-700 (3] 512px for
200k steps. Samples are fully uncurated and generated with cfg 3.0.
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The MART
Teaee Per
Figure 15: Comparison of DFM against baselines DiT-XL trained Kinetics-700 (3] 512px for
200k steps. Samples are fully uncurated and generated with cfg 3.0.
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FLUX-DFM
FLUX-FT
FLUX-DFM
FLUX-FT
FLUX-DFM
FLUX-FT
7
KEEP OFF GRASS
KEEP OFF
THE GRASS
Figure 16: Comparison finetuning FLUX-DEV with DFM against standard full finetuning trained
finetuned for 24k steps. Samples are generated with cfg 4.5.
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FLUX-DFM
FLUX-FT
FLUX-DFM
FLUX-FT
FLUX-DFM
FLUX-FT
BONEZ
7
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Figure 17: Comparison finetuning FLUX-DEV with DFM against standard full finetuning trained finetuned for 24k steps. Samples are generated with cfg 4.5.
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Sampling Steps Siago
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Figure 18: Ablation of per-stage sampling steps on DiT-XL trained on ImageNet- 1K 512px [5] for 500k steps. Samples are selected highlight the effects of varying sampling parameters. Samples generated with cfg 3.0.
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Sampling Stnge Threshold
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Figure 19: Ablation of the effect of cfg values and sampling threshold 7 DÍT-XI. trained on ImageNet- 512px (5) for 500k steps. Samples are selected to highlight the effects of varying sampling parameters. Samples are generated with cfg 3.0.
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Figure 20: Qualitative results from selected classes on ImageNet-IK [5] 512px produced by DiT-XL
trained with DFM for 1.3M steps. We use 30 and 10 sampling steps respectively for the first and second stages and a cfg value of 3.0.
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Figure 21: Qualitative results from selected classes on ImageNet- IK [5] 512px produced by DiT-XL trained with DFM for 1.3M steps. We use 30 and 10 sampling steps respectively for the first and second stages and a cfg value of 3.0.
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Figure 22: Qualitative results from selected classes on ImageNet-IK [5] 512px produced by DiT-XL trained with DFM for 1.3M steps. We use 30 and 10 sampling steps respectively for the first and second stages and a cfg value of 3.0.
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Figure 23: Fully uncurated samples from ImageNet- IK (5) 512px produced by DiT-XL trained with DFM for 1.3M steps. We use 30 and 10 sampling steps respectively for the first and second stages and cfg value of 3.0.
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USS
BPAOOA
BESE KONI
F7
SUWELI
TRUOKK
SEVENTCE
9:3
Figure 24: Fully uncurated samples from ImageNet- IK (5) 512px produced by DiT-XL trained with DFM for 1.3M steps. We use 30 and 10 sampling steps respectively for the first and second stages and cfg value of 3.0.
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SR. U2TOT GEE
1798 ZERTI
Figure 25: Fully uncurated samples from ImageNet- IK (5) 512px produced by DiT-XL trained with DFM for 1.3M steps. We use 30 and 10 sampling steps respectively for the first and second stages and cfg value of 3.0.
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42


Reviews:
[{"review_id": "z7cay7sFKV", "reviewer": "Reviewer_hhY3", "summary": "This paper proposes a progressive generative modeling framework on top of flow matching. The approach first applies a user-defined decomposition to the input image and produces multi-scale representations. Then the flow matching is used to model individual scale representation independently. The sampling procedure generates images progressively by traversing through different scale predictions. The paper claims that the proposed approach avoids requiring expert models or ad hoc designs and improves image and video generation performance significantly.", "questions": "I don't follow progressive modeling literatures and would like to hear more from other reviewers regarding novelty. I am open to adjust rating.", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 2, "strengths_and_weaknesses": "**Strength**\n\n1. The writing is smooth and easy to follow.\n\n2. The paper is tackling an interesting problem by decomposing diffusion generation tasks into simpler subtasks through progressive modeling.\n\n**Weakness**\n1. Through the paper advocates that the proposed framework avoids the need for custom diffusion formulation, ad-hoc sampler, etc., it highly relies on properly defined multi-scale representations. The paper puts that various techniques can be used like DWT, DCT, or Fourier transforms, while how to determine the number of scales and the size of scales for these approaches is unclear. No principled approach is provided.\n2. The paper claims that the progressive modeling achieves better generation performance than Flow Matching. Does this improvement come with greater complexity for training and inference? The framework needs to model muti-scale distributions during training and the sampling also progressively traverses multiple stages. During training, do you sample time steps for different scales jointly? Does that need a lot of samples to approximate the $p_t$ expectation?\n3. Typos: add-hoc samplers (in Abstract), and the formulate the .... (line 140), etc.", "was_revised": true, "final_justification": "The additional experimental results provided by the authors are appreciated. I maintain my rating and lean toward acceptance.", "rebuttal": "We thank all reviewers for their thoughtful feedback. We are encouraged that the paper received positive assessments. Reviewers Nk2B and uRBr described the method as interesting, neat, novel, and original. Reviewer hhY3 found the presentation clear and easy to follow, and Reviewer 6uMG emphasized that the approach is both simple and straightforward to implement. Moreover, reviewers 6uMG and Nk2B found our experiments to be extensive and the method to deliver strong performance.\nBelow, we provide detailed responses to Review hhY3 questions and concerns. \n\n**Question 1**\n\n>Through the paper advocates that the proposed framework avoids the need for custom diffusion formulation, ad-hoc sampler, etc., it highly relies on properly defined multi-scale representations. The paper puts that various techniques can be used like DWT, DCT, or Fourier transforms, while how to determine the number of scales and the size of scales for these approaches is unclear. No principled approach is provided.\n\nFollowing the Reviewer’s comment, we validate robustness of our suggested Laplacian hyperparameters to diverse decompositions and autoencoders.\n\nDMF relies on a multi-scale spatial representation that separates low- and high-frequency information. Such separation can be achieved with several decomposition methods such as Laplacian, DCT, DWT, etc, by decoding the low- and high-frequency components separately.  Despite their representational differences, we find the practical guidance on choosing the hyper-parameters in Appendix A.5 still applies. We retrained DFM with DCT‑ and DWT‑based decompositions using exactly the same settings as in Table 2. As reported in Table R1, these identical hyper‑parameters deliver the same gains over the Flow‑Matching baseline for every decomposition. We further validate that these conclusions hold irrespective of the autoencoder representation. When we adopt the CogVideo autoencoder and train with identical hyper-parameters, DFM equipped with Laplacian, DCT, or DWT outperforms the baseline by a wide margin (Table R2). We have updated the paper to include these results and expand the discussion on the choice of the decomposition method.\n\n**Table R1:** Quantitative comparison of DFM equipped with various decomposition methods, trained on ImageNet 512px with a DiT-XL/2 backbone and scale-equavariant FLUX AE. Numbers correspond to CFG values of 1.0, 1.25 and 1.5.\n\n| Experiment        | FID_50k (1.0 / 1.25 / 1.5)    | FDD_50k (1.0 / 1.25 / 1.5)       | IS (1.0 / 1.25 / 1.5)             |\n|------------------|-------------------------------|----------------------------------|-----------------------------------|\n| Flow Matching     | 15.89 / 7.59 / 4.73           | 282.9 / 185.7 / 132.5            | 58.5 / 97.2 / 138.9               |\n| Ours (DWT)        |    9.48 /  4.20 / 4.40           | 195.6 / 117.3 / 84.8       |  78.8 / 136.9 / 199.2     |\n| Ours (DCT)        | 9.60 / 4.19 / 4.37            | 194.4 / 115.1 / 82.5            | 78.6 / 138.3 / 201.2           |\n| Ours (Laplacian)  | 9.77 / 4.28 / 4.28            | 200.6 / 120.0 / 85.8             | 77.9 / 135.6 / 196.8              |\n\n**Table R2:** Quantitative comparison of DFM with CogVideo AE, equipped with various decomposition methods, and trained on ImageNet 512px with a DiT-XL/2 backbone. Numbers correspond to CFG values of 1.0, 1.25 and 1.5.\n\n| Experiment        | FID_50k (1.0 / 1.25 / 1.5)    | FDD_50k (1.0 / 1.25 / 1.5)       | IS (1.0 / 1.25 / 1.5)             |\n|------------------|-------------------------------|----------------------------------|-----------------------------------|\n| Flow Matching     | 16.94 / 8.59 / 5.84           | 319.8 / 218.4 / 159.5         | 58.5 / 96.0 / 137.3            |\n| Ours (DWT)        |   8.72 / 4.26 / 5.08             | 206.9 / 124.5 / 89.2           |  92.3 / 159.2 / 223.5        |\n| Ours (DCT)        | 8.75 / 4.33 / 5.18            | 207.5 / 125.8 / 90.0          | 92.5 / 158.4 / 223.0             |\n| Ours (Laplacian)  | 8.80 / 4.36 / 5.14            | 208.4 / 125.7 / 90.2          | 91.7 / 158.8 / 222.0           |\n\n**Question 2**\n> The paper claims that the progressive modeling achieves better generation performance than Flow Matching. Does this improvement come with greater complexity for training and inference?\n\nWhile our proposed method maintains **identical training compute** as the baselines, it indeed introduces additional components compared to single-stage models such as Flow Matching. However, some added complexity is an inherent trade-off in progressive modeling. Previous progressive generators improve the performance over the single-scale models but introduce a large degree of complexity such as using multiple models (e.g. Cascaded Models), or incorporating renoising tricks as in Pyramidal Flow (See L. 33-39). A main design principle of DFM is to improve the benefits of progressive models while reducing such complexities by using a **single model, and a training objective and denoising process** closely following single-scale methods. The main additional components introduced by DFM are limited to (i) lightweight decomposition step with an off-the-shelf method (e.g. Laplacian), (ii) sampling multiple timesteps (rather than one), (iii) additional lightweight patchification layers and (iii) maintaining extra hyper-parameters. In practice, these changes are concise and introduce only a marginal time overhead of 1.2% in a single training iteration. We have provided in Appendix A.5 concrete guidance on setting hyperparameters and showed in the paper that following these choices, DFM consistently achieves superior performance on a wide range of generative tasks including image and video generation, and large scale text-to-Image synthesis. We also demonstrated that, under identical hyper-parameters, our method is generalizable to different resolutions (see Table. 2 of the main paper) and different autoencoder and decomposition methods (see our response to Question 1).\n\n**Question 3**\n> During training, do you sample time steps for different scales jointly? Does that need a lot of samples to approximate the $p_t$ expectation?\n\nDFM operates on different stages, where each stage contains multi-scale representations. For instance, for the first stage modeling, only the first (low-frequency) scale is modeled, while in the second stage, both scales (low and high frequency) are jointly modeled. During training, we first sample the stage number from a discrete probability distribution (L. 158). Then, we sample the timesteps of different scales **independently** (L.140), where each scale’s timestep is drawn from a **predetermined** logit-normal distribution, parametrized by a location (m_s), where s is the scale index within the sampled stage. We ablated over the choice of m_s in Table. 2 (b), and found that it is beneficial to have the distribution of the **last scale** to use location (m_s=0), aligning with common practice in flow matching [1-4], while shifting the location of **earlier scales** toward lower noisy levels (higher m_s value). This better simulates the inference-time behavior where during the generation of scale s, the previous scale s−1 has already undergone significant denoising from previous stages. Please see Section 4.2 (\"Training timestep distribution\") for more details.\n\nTo clarify this, we have revised Eq. (4) as follows:\n\n$$\n\\\\mathcal{L}\n  = E_{Q\\\\sim p_{q},\\\\; t^{1}\\\\sim p_{t, Q}^{1},\\\\dots,t^{S}\\\\sim p_{t, Q}^{S},\\\\; X_{1}\\\\sim p_{d},\\\\; X_{0}\\\\sim p_{n}}\n    \\\\sum_{s=1}^{S}\n      M^{s}\\\\,\n      \\\\left\\\\lVert\n        \\\\mathcal{G}\\\\bigl(P_{t^{1},\\\\dots,t^{S}},\\\\,t^{1},\\\\dots,t^{S}\\\\bigr)\n        - v^{s}\n      \\\\right\\\\rVert_{2}^{2}\\\\,.\n$$\n\nHere, we introduced a new notation Q that corresponds to the stage number (corresponding to the number of modeled scales) for the current training iteration, and revised the discrete distribution notation to $p_q$. $p_{t, Q}^s$ denotes the timestep distribution of the scale s within stage Q. In DFM, for the two scales case ($Q=2$), $p_{t,Q}^1$ follows a logit-normal distribution with location $m_{1} = 0 $ and $p_{t,Q}^0$ follows a logit-normal distribution with location $m_{0} = 1.5$. \n\nBelow, we include a pseudo code of the time step sampling, which we will include in the paper for better clarity.\n\n$$\n\\\\begin{array}{l}\n\\\\mathrm{procedure}\\\\;SampleTrainingTimesteps(S):\\\\\\\\\n\\\\mathrm{inputs:}\\\\;S \\\\text{    ; total number of scales}\\\\\\\\\n\\\\mathrm{outputs:}\\\\;(t^{1},\\\\ldots,t^{S})\\\\\\\\[6pt]\nQ\\\\leftarrow\\\\mathrm{SampleDiscreteDistribution}(p_{q}) \\\\text{ ; stage index corresponding to number of modeled scales}\\\\\\\\\nt^{Q}\\\\leftarrow\\\\mathrm{SampleLogitNormal}(m=0)\\\\\\\\\n\\\\mathrm{for}\\\\;s=1\\\\;\\\\mathrm{to}\\\\;Q-1:\\\\\\\\\n\\\\quad t^{s}\\\\leftarrow\\\\mathrm{SampleLogitNormal}(m=1.5)\\\\\\\\\n\\\\mathrm{end\\\\;for}\\\\\\\\\n\\\\mathrm{for}\\\\;s=Q+1\\\\;\\\\mathrm{to}\\\\;S:\\\\\\\\\n\\\\quad t^{s}\\\\leftarrow 0\\\\\\\\\n\\\\mathrm{end\\\\;for}\\\\\\\\\n\\\\mathrm{return}\\\\;(t^{1},\\\\ldots,t^{S})\n\\\\end{array}\n$$\n\nWe have revised the method section to better distinguish between “stage” and “scale” and clarify the timestep sampling strategy. We hope that this answers the reviewer’s concern and we remain available to clarify further if needed.\n\n**Question 4**\n> Typos: add-hoc samplers (in Abstract), and the formulate the .... (line 140), etc.\n\nWe thank the reviewer for finding the typos. We corrected them in our revised version and performed an additional pass of proofreading.\n\n**References**\n\n[1] Scaling Rectified Flow Transformers for High-Resolution Image Synthesis, ICML 2024\n\n[2] FasterDiT: Towards Faster Diffusion Transformers Training without Architecture Modification, NeurIPS 2024\n\n[3] SnapGen: Taming High-Resolution Text-to-Image Models for Mobile Devices with Efficient Architectures and Training, CVPR 2025\n\n[4] Wan: Open and Advanced Large-Scale Video Generative Models, 2025"}, {"review_id": "ajc1Vhoj9F", "reviewer": "Reviewer_6uMG", "summary": "In this paper, the authors propose a progressive generation framework for high-dimension images and videos. They use a Laplacian decomposition strategy to produce a multiscale input representation. The proposed Decomposable Flow Matching (DFM) applies flow matching independently at each level of a user-defined multi-scale representation. In addition, extensive experiments show the effectiveness of the proposed method across various tasks.", "questions": "See Weakness.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths\n+ The proposed method is simple and easy to implement. It is agnostic to the choice of decompositions and does not need multiple models or per-stage training.\n+ The experiments is extensive and the performance gain is large. This paper provides a comprehensive analysis of critical training and sampling hyperparameters. In addition, the proposed method outperforms existing sota methods across various tasks.\n\nWeaknesses\n- For latent space, we re-train all autoencoders by scale-equivariant finetuning. To my knowledge, this can boost the generation performance. Regarding the baselines in Section 4.4, do they also employ scale-equivariant autoencoders? If not, the comparison may be unfair.\n- lognorm location in Table 1 (b). First, there appears to be a potential typo: “second stage” should likely be “first stage.” Second, the main text states that a location value of 1.5 is selected. However, according to Table 1(b), this setting does not yield the best performance. What is the rationale behind choosing 1.5?", "was_revised": true, "final_justification": "While my concerns have been adequately addressed, I still find the overall contribution to be borderline in terms of novelty and impact. Therefore, I maintain my score at Borderline Accept.", "rebuttal": "We thank all reviewers for their thoughtful feedback. We are encouraged that the paper received positive assessments. Reviewers Nk2B and uRBr described the method as interesting, neat, novel, and original. Reviewer hhY3 found the presentation clear and easy to follow, and Reviewer 6uMG emphasized that the approach is both simple and straightforward to implement. Moreover, reviewers 6uMG and Nk2B found our experiments to be extensive and the method to deliver strong performance.\nBelow, we provide detailed responses to Review 6uMG questions and concerns. \n\n**Question 1**\n> For latent space, we re-train all autoencoders by scale-equivariant finetuning. To my knowledge, this can boost the generation performance. Regarding the baselines in Section 4.4, do they also employ scale-equivariant autoencoders? If not, the comparison may be unfair.\n\nWe confirm that all baselines in Section 4.4 employ the **same scale-equivariant autoencoders**.  We additionally provide in **Appendix. D** a comparison of our method against vanilla Flow Matching, where both use the **standard FLUX autoencoder** (i.e. without scale-equivariance finetunning) and show an even wider margin of improvement for our method. To further demonstrate the generality of DFM across different autoencoder representations, we re-train DFM and Flow Matching using the same settings as in Table. 2 but using the **standard Cogvideo autoencoder** (i.e. without scale-equanariance finetunning). As reported in Table. R3, DFM continues to show similar improvement over Flow Matching. We revised section 4.1 to make it clear that all baselines employ the same autoencoder.\n\n**Table R3:** Quantitative comparison of DFM with CogVideo AE, trained on ImageNet 512px with a DiT-XL/2 backbone. Numbers correspond to CFG values of 1.0, 1.25 and 1.5.\n\n| Experiment             | FID ↓(1.0 / 1.25 / 1.5)     | FDD ↓ (1.0 / 1.25 / 1.5)           | IS ↑ (1.0 / 1.25 / 1.5)             |\n|------------------------|----------------------------|----------------------------------|-----------------------------------|\n| FlowMatch (CogVideo AE)| 16.94 / 8.59 / 5.84        | 319.88 / 218.48 / 159.51         | 58.56 / 96.08 / 137.39            |\n| DFM (CogVideo AE)      | 8.80 / 4.36 / 5.14         | 208.4 / 125.73 / 90.22           | 91.79 / 158.80 / 222.09           |\n\n**Question 2**\n> lognorm location in Table 1 (b). First, there appears to be a potential typo: “second stage” should likely be “first stage.”\n\nWe thank the reviewer for pointing this out. During the first stage, only the first scale (low-frequency) is generated. During the second stage, two scales are generated simultaneously: the previous (low-frequency scale), which will be close to being fully denoised, and the current (high-frequency scale). In Table 1 (b), we are referring to the first scale timestep distribution during second stage training. We have revised the table caption to “Previous scale lognorm location” and clarified in Sec. 4.2 the intended meaning. Please refer to our answer to Reviewer hhY3 Question 3 for more general clarifications regarding timestep sampling\n\n**Question 3**\n> Second, the main text states that a location value of 1.5 is selected. However, according to Table 1(b), this setting does not yield the best performance. What is the rationale behind choosing 1.5?\n\nWe found that location values of 0.5, 1.0, and 1.5 yield comparable performance, with differences of less than **1% in FDD** and **1.3% in IS** (as reported in Table 1 (b)) when ablations are conducted on DiT/B. A larger location value, however, simulates availability of a cleaner first scale (low-frequency) result and aligns more closely to inference time behavior, where the second generation stage is started once the first stage is close to being fully denoised. We hypothesize that under the increased DiT/XL capacity used in the main experiments, a closer alignment to inference-time behavior would be beneficial. Since Table 1(b) suggests that any location value within the range 0.5–1.5 yields similarly strong results, we prefer choosing 1.5. We briefly discussed this in **Lines 226–228** and have now revised the text in that section to better clarify our rationale."}, {"review_id": "7ACejE74uA", "reviewer": "Reviewer_Nk2B", "summary": "Decomposable Flow Matching (DFM) use a multi-scale learning to learn different resolutions (Laplacian pyramid). Given all noisy images at different scale on different noise levels, predict the per-scale velocities. At inference, progressively generates from low-res to high-res while conditioning on all finished resolutions. They use different patch sizes to handle the multi-scale within a single model. They fine-tune existing image and video autoencoders for any-resolution before training their models.", "questions": "- Any intuition why 256->512-> 1024 was worse?\n- why logit-normal over uniform for t?", "limitations": "Yes, mainly the hyperparameters.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 1, "significance": 3, "originality": 4, "strengths_and_weaknesses": "- Multi-scale progressive growing within a single model is very neat compared to the engineering-heavy cascaded approach.\n- FID not FDD in abstract\n- The results are strong and the method is much cleaner than cascaded diffusion. This is very good.\n- The biggest weakness of the paper is that its not well written, the authors should really make an effort to improve the clarity of the work. \n- Its not clear or well explained how the distribution of t is chosen, why is it logit-normal? The visualization from figure 2b time-step sampling should be shown in 4.2.\n- Section 4.2 is weird, why are we only learning more about the distribution of t in the experiments sections, when it should be clarified in the methods with a nice figure.\n- In the ablations it would be great to see what happens with regular uniform distribution for t\n- This work will be high-impact as it makes cascaded diffusion obsolete, since this is much simpler and cleaner training all-in-one with better results", "was_revised": true, "final_justification": "The authors have done extra ablations and reorganized the paper (although I cannot see it) based on my comments to improve the paper. I am satisfied and leaving my score as \"accept\".", "rebuttal": "We thank all reviewers for their thoughtful feedback. We are encouraged that the paper received positive assessments. Reviewers Nk2B and uRBr described the method as interesting, neat, novel, and original. Reviewer hhY3 found the presentation clear and easy to follow, and Reviewer 6uMG emphasized that the approach is both simple and straightforward to implement. Moreover, reviewers 6uMG and Nk2B found our experiments to be extensive and the method to deliver strong performance.\nBelow, we provide detailed responses to Review Nk2B questions and concerns. \n\n**Question 1**\n> FID not FDD in abstract\n\nWe refer to Frechet DINOv2 Distance (FDD) in the abstract. On ImageNet 512px with CFG=1.5, the base architecture (Flow Matching) achieves an FDD of 132.5 while DFM reports 85.8, marking 35.2% relative improvement. We have revised the abstract to spell out the full metric name and specify the CFG value used for these results.\n\n\n**Question 2**\n> Its not clear or well explained how the distribution of t is chosen, why is it logit-normal? \n\n> In the ablations it would be great to see what happens with regular uniform distribution for t\n\n> why logit-normal over uniform for t?\n\nThe logit-normal timestep distribution was first introduced in Stable Diffusion 3 [1], and its effectiveness has been verified in following work [2]. It has become a standard approach for timestep sampling in the latest diffusion-based methods [3-6]. Motivated by this, we adopted the logit-normal distribution throughout our paper. As suggested, we conducted additional experiments replacing logit-normal sampling with uniform sampling for both the Flow Matching baseline and DFM. As reported in Table R4, we observe a consistent drop in performance for both models, confirming the advantage of the logit-normal distribution. We will include these results in the supplementary material.\n\n**Table R4:** Ablations of DFM and Flow Matching with uniform and logit-normal timestep distribution, trained on ImageNet 512px with a DiT-B/2 backbone. \n| Baseline                     | FID ↓   | FDD ↓     | IS ↑    |\n|-----------------------------|---------|-----------|---------|\n| Flow Matching w/ logit-normal | 38.01   | 665.16    | 30.52   |\n| Flow Matching w/ uniform      | 45.61   | 834.92    | 26.48   |\n| DFM w/ logit-normal           | 29.83   | 567.21    | 40.38   |\n| DFM w/ uniform                | 32.87   | 651.09    | 36.23   |\n\n**Question 3**\n> The biggest weakness of the paper is that its not well written, the authors should really make an effort to improve the clarity of the work.\n\nWe thank the Reviewer for their feedback. We understand from the Reviewer’s punctual comments that the source of the clarity issues resides in the discussion of the adopted timestep distributions. Below, we include clarifications on the timestep sampling. \n\n**Timestep Sampling**\n\nDFM operates on different stages, where each stage contains multi-scale representations. For instance, for the first stage modeling, only the first (low-frequency) scale is modeled, while in the second stage, both scales (low and high frequency) are jointly modeled. During training, we first sample the stage number from a discrete probability distribution (L. 158). Then, we sample the timesteps of different scales independently (L. 140), where each scale’s timestep is drawn from a predetermined logit-normal distribution, parametrized by a location ($ m_s $), where s is the scale index within the sampled stage. We ablated over the choice of $m_s$ in Table. 2 (b), and found that it is beneficial to have the distribution of the last scale to use location ($m_s=0$), aligning with common practice in flow matching [1-6], while shifting the location of earlier scales toward lower noisy levels (higher $m_s$ value). This better simulates the inference-time behavior, where during the generation of scale s, the previous scale s−1 has already undergone significant denoising from previous stages. Please see Section 4.2 (\"Training timestep distribution\") for more details.\n\nWe have revised Eq. (4) to better show that timesteps are sampled independently and that the timestep distribution depends on the stage number and scale index within that stage.\n\n$$\n\\\\mathcal{L}\n  = E_{Q\\\\sim p_{q},\\\\; t^{1}\\\\sim p_{t, Q}^{1},\\\\dots,t^{S}\\\\sim p_{t, Q}^{S},\\\\; X_{1}\\\\sim p_{d},\\\\; X_{0}\\\\sim p_{n}}\n    \\\\sum_{s=1}^{S}\n      M^{s}\\\\,\n      \\\\left\\\\lVert\n        \\\\mathcal{G}\\\\bigl(P_{t^{1},\\\\dots,t^{S}},\\\\,t^{1},\\\\dots,t^{S}\\\\bigr)\n        - v^{s}\n      \\\\right\\\\rVert_{2}^{2}\\\\,.\n$$\n\nHere, we introduced a new notation Q that corresponds to the stage number (corresponding to the number of modeled scales) for the current training iteration, and revised the discrete distribution notation to $p_q$. $p_{t, Q}^s$ denotes the timestep distribution of the scale s within stage Q. In DFM, for the two scales case ($Q=2$), $p_{t,Q}^1$ follows a logit-normal distribution with location $m_{1} = 0 $ and $p_{t,Q}^0$ follows a logit-normal distribution with location $m_{0} = 1.5$. \n\nBelow, we include a pseudo code of the time step sampling, which we will include in the paper for better clarity.\n\n$$\n\\\\begin{array}{l}\n\\\\mathrm{procedure}\\\\;SampleTrainingTimesteps(S):\\\\\\\\\n\\\\mathrm{inputs:}\\\\;S \\\\text{    ; total number of scales}\\\\\\\\\n\\\\mathrm{outputs:}\\\\;(t^{1},\\\\ldots,t^{S})\\\\\\\\[6pt]\nQ\\\\leftarrow\\\\mathrm{SampleDiscreteDistribution}(p_{q}) \\\\text{ ; stage index corresponding to number of modeled scales}\\\\\\\\\nt^{Q}\\\\leftarrow\\\\mathrm{SampleLogitNormal}(m=0)\\\\\\\\\n\\\\mathrm{for}\\\\;s=1\\\\;\\\\mathrm{to}\\\\;Q-1:\\\\\\\\\n\\\\quad t^{s}\\\\leftarrow\\\\mathrm{SampleLogitNormal}(m=1.5)\\\\\\\\\n\\\\mathrm{end\\\\;for}\\\\\\\\\n\\\\mathrm{for}\\\\;s=Q+1\\\\;\\\\mathrm{to}\\\\;S:\\\\\\\\\n\\\\quad t^{s}\\\\leftarrow 0\\\\\\\\\n\\\\mathrm{end\\\\;for}\\\\\\\\\n\\\\mathrm{return}\\\\;(t^{1},\\\\ldots,t^{S})\n\\\\end{array}\n$$\n\nWe have also implemented paper modifications according to each of the Reviewer’s punctual comments and remain available to further modify the manuscript in case this does not fully address the clarity issues.\n\n**Question 4**\n> The visualization from figure 2b time-step sampling should be shown in 4.2.\n\nAs per the Reviewer's suggestion, we improved the clarity of the discussion in Sec 4.2 and supplement it with an inset figure visualizing the training timestep distribution of each scale in every stage and the effects of changing the distribution location hyperparameter. Due to NeurIPS rebuttal rules, however, we are unable to attach the new figure here. \n\n**Question 5**\n> Section 4.2 is weird, why are we only learning more about the distribution of t in the experiments sections, when it should be clarified in the methods with a nice figure.\n\nWe thank the Reviewer for the suggestion. We introduced **in the method section (3.3)**, the inference timestep scheduler (L. 148-154) and the training timestep distribution (L. 155-163), where we explained that after sampling the stage number according to a discrete probability distribution, the timesteps of each scale are sampled independently. The timestep corresponding to the last scale of each stage follows a logit-normal distribution, while the timestep corresponding to previous scales follows the same logit-normal distribution but shifted towards lower noise levels. Since the amount of shifting is a hyperparameter derived empirically, we discuss its value in the experiments section to support it with an ablation study (Tab. 1 (b)). Following the Reviewer’s suggestion, we supplemented Section 4.2 with a figure showing the exact distribution of the training timestep of each scale in every stage in accordance with the ablated “location” hyper-parameter. \n\n**Question 6**\n> Any intuition why 256->512-> 1024 was worse?\n\nWe hypothesize that the performance gap between the “256->512->1024” and “256->1024” experiment in Tab. 2 (f) comes from differences in stage sampling probabilities during training $p_q$ (as ablated in Tab. 1 (a) for the 2 stages setting). In the ablation experiment of Tab. 1 (f), stage sampling probabilities are set as follows:\n- 512->1024: (0.9, 0.1)\n- 256->512->1024: (0.8, 0.1, 0.1)\n- 256->1024: (0.9, 0.1)\n\nThe (0.8, 0.1, 0.1) choice for the “256->512->1024” experiment was operated to match the “512->1024” experiment's second-stage sampling probabilities, with the effect of undermining low-frequency training.\nTo verify this hypothesis, we repeat the experiment, setting the “256->512->1024” stage sampling probabilities during training to (0.9, 0.05, 0.05), thus matching the best-performing “256->1024” experiment in the low-frequency training. At inference time, we also vary sampling steps per stage from (20, 12, 8) respectively for each stage, to (25, 10, 5), bringing it closer to the 2-stage setting of (25, 15). As shown in Table R5, the performance gap between “256->512->1024” and “256->1024” is no longer present, and 3 stages deliver slightly improved performance.\n\n**Table R5:** Ablations of three-stage DFM, trained on ImageNet 1024px with a DiT-B/2 backbone. Numbers correspond to CFG values of 1.0.\n| Baseline                         | FID ↓   | FDD ↓   | IS ↑    |\n|----------------------------------|---------|---------|---------|\n| 2 stages                         | 41.06   | 704.0   | 30.9    |\n| 3 stages (0.8, 0.1, 0.1)         | 50.61   | 827.0   | 24.5    |\n| 3 stages (0.9, 0.05, 0.05)       | 40.6    | 683.2   | 31.82   |\n\n**References**\n\n[1] Scaling Rectified Flow Transformers for High-Resolution Image Synthesis, ICML 2024\n\n[2] FasterDiT: Towards Faster Diffusion Transformers Training without Architecture Modification, NeurIPS 2024\n\n[3] SnapGen: Taming High-Resolution Text-to-Image Models for Mobile Devices with Efficient Architectures and Training, CVPR 2025\n\n[4] Wan: Open and Advanced Large-Scale Video Generative Models, 2025\n\n[5] Movie Gen: A Cast of Media Foundation Models, 2024\n\n[6] Seedance 1.0: Exploring the Boundaries of Video Generation Models, 2025"}, {"review_id": "pWldQWDpHy", "reviewer": "Reviewer_uRBr", "summary": "The paper introduces Decomposable Flow Matching (DFM), a novel generative modeling framework that decomposes an input into multiple coarse-to-fine scales and apply flow matching jointly to those components. The authors mainly focused on the Laplacian pyramid and show that DFM reports substantial gains across benchmarks.", "questions": "The sampling schedule used at inference time appears interesting. The threshold values (0.7/0.95) suggest that the model spends the majority of its sampling steps on the low-frequency component, with relatively few steps allocated to the high-frequency component. This raises the question of whether performance might improve by fully denoising the low-frequency component first, before proceeding to the high-frequency component, which is similar in spirit to a cascaded model, but with both stages handled by the same model rather than separate ones.", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "## Strengths\n- The key idea of applying flow matching at multiple scales in a single model is interesting and novel. \n- Unlike cascaded models, DFM uses a single network to handle all components of the image.\n- The ablation study is well carried out.\n\n## Weaknesses\n- The comparative evaluations against baseline models are conducted under a fixed training budget, which is reasonable. However, a deeper analysis of training and inference complexity is necessary. Specifically, DFM’s design feeds all image components into the DiT simultaneously. Although these components have different patch sizes to alleviate the problem, their joint processing could increase memory usage, as each token must attend to all components. For instance, a two-stage DFM would effectively double the number of patches and could potentially quadruple attention computation if I understand correctly, which leads to significantly higher memory requirements and slower training. Could the authors elaborate on that and provide an additional analysis reporting memory usage and training/inference speeds compared to baseline models?", "was_revised": true, "final_justification": "After reading the rebuttal and the other reviewers’ comments, I believe this is a good piece of work, and I lean toward accepting the paper.", "rebuttal": "We thank all reviewers for their thoughtful feedback. We are encouraged that the paper received positive assessments. Reviewers Nk2B and uRBr described the method as interesting, neat, novel, and original. Reviewer hhY3 found the presentation clear and easy to follow, and Reviewer 6uMG emphasized that the approach is both simple and straightforward to implement. Moreover, reviewers 6uMG and Nk2B found our experiments to be extensive and the method to deliver strong performance.\nBelow, we provide detailed responses to Review uRBr questions and concerns. \n\n**Question 1**\n>  Specifically, DFM’s design feeds all image components into the DiT simultaneously. Although these components have different patch sizes to alleviate the problem, their joint processing could increase memory usage, as each token must attend to all components. For instance, a two-stage DFM would effectively double the number of patches and could potentially quadruple attention computation if I understand correctly, which leads to significantly higher memory requirements and slower training. Could the authors elaborate on that and provide an additional analysis reporting memory usage and training/inference speeds compared to baseline models?\n\nWe thank the reviewer for their question. DFM aggregates token representations from different scales by summing them before input to the transformer block (Lines 180–181), thus preserving the same memory and compute requirements as the baseline. This is possible since we maintain a consistent number of tokens across scales by adjusting the patch size (L. 176-179). In Table R6, we compare DFM with Flow Matching in terms of peak CUDA memory usage, GFLOPs, forward and training iterations latency, and sampling time (including decoding the image). As shown, DFM introduces only a small overhead. We have included these results in the Appendix.\n\n**Table R6:** Comparison of DFM efficiency compared with Flow Matching measured on 512px Image input and batch size 1.\n| Model          | # Params   | Peak Memory  | GFLOPs  | Forward Latency  | Train Iter Speed  | Sampling Time  |\n|----------------|------------|----------------|-----------|--------------------|---------------------|------------------|\n| Flow Matching  | 712.122 M  | 6.258 GB       | 524.613   | 60.25 ms           | 297.39 ms           | 2.43 s           |\n| DFM            | 716.482 M  | 6.294 GB       | 524.638   | 61.32 ms           | 301.00 ms           | 2.43 s           |\n\n\n> The sampling schedule used at inference time appears interesting. The threshold values (0.7/0.95) suggest that the model spends the majority of its sampling steps on the low-frequency component, with relatively few steps allocated to the high-frequency component. This raises the question of whether performance might improve by fully denoising the low-frequency component first, before proceeding to the high-frequency component, which is similar in spirit to a cascaded model, but with both stages handled by the same model rather than separate ones.\n\nWe thank the reviewer for their observation. We have indeed explored fully denoising the first (low-frequency) scale before proceeding with the second (high-frequency) stage, and reported the results in **Figure 3 (a)** (denoted as $\\\\tau=1.0$). However, we found this setting to underperform compared to $\\\\tau=0.7$. We hypothesize that $\\\\tau=1.0$ introduces a degree of train-test mismatch between stages, leading to degraded performance. Such train-test mismatch is alleviated at larger CFG values.\n\nWe also note that compared to a cascaded model, a core difference of DFM is that it also restricts the second stage to only generate the high-frequency information, whereas cascaded models generate the full image from scratch in the second stage, conditioned on the first stage output."}]

Author rebuttal:

Meta-review: This paper proposed a progressive generative modeling framework, termed Decomposable Flow Matching (DFM), built atop flow matching techniques. The core idea is as follows: DFM decomposes input images (or videos) into multi-scale representations using user-defined strategies (e.g., Laplacian pyramid, DWT, DCT, Fourier transforms). Flow matching is then applied independently at each scale, allowing the model to learn and generate at different resolutions. During sampling, the model generates images progressively, traversing from coarse to fine scales. The authors claim that this approach avoids the need for expert-designed models or ad hoc samplers. The authors also show experimentally that DFM achieves significant improvements in image and video generation quality.

The paper has two main strengths:

- DFM is conceptually simple, easy to implement, and agnostic to the choice of decomposition. As a result, DFM could be widely applicable.
- DFM has significant performance gains over state-of-the-art methods on multiple benchmarks, with comprehensive ablations and analysis of hyperparameters. The evaluation is thorough, covering various tasks, and includes analysis of critical design choices (e.g., time-step distributions, scale selection). The approach could make cascaded diffusion models obsolete by offering a cleaner, more effective alternative.

The paper has the following weaknesses:

- The review team noted that the paper is not well written, with unclear explanations of key design choices, including the rationale for the logit-normal distribution for time-step sampling, and the details of the multi-scale decomposition. The paper also suffers from typos and formatting issues that detract from the paper’s professionalism.
- The paper lacks a principled approach for selecting the number and size of scales, and it shifts the difficulty of choosing these parameters to the users.
- There are concerns about fairness in baseline comparisons, particularly regarding the use of scale-equivariant autoencoders in the proposed method but not in baselines. Some ablations are missing, such as the effect of using a uniform distribution for time-step sampling.
- While the method is original in its unified approach, some reviewers feel the novelty is incremental, as progressive modeling and multi-scale decompositions are established ideas.

Overall, the review team has a positive assessment of the paper (3 weak accept, 1 accept). The consensus is that DFM is a clear step forward in simplifying and improving progressive generative modeling, and that the empirical results are strong and well-supported. 

As a final note, I encourage the authors to revise the paper for clarity, provide more principled guidance on decomposition choices, and ensure fair baseline comparisons. With these improvements, the work could have a broader impact.
Decision: Accept (poster)