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arxiv: 2606.10450 · v1 · pith:XAWKSEHGnew · submitted 2026-06-09 · 💻 cs.CV · cs.LG

Few-step Generative Models as Lossy Compression

Fuma Kimishima , Jinjia Zhou This is my paper

Pith reviewed 2026-06-27 14:10 UTC · model grok-4.3

classification 💻 cs.CV cs.LG
keywords lossy compressionfew-step generative modelsrectified flowconsistency trajectory modelsmeanflowreverse channel codingdiffusion modelsimage compression
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The pith

Few-step generative models can serve as lossy image compressors without retraining by adapting them to reverse channel coding.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines whether Rectified Flow, Consistency Trajectory Models, and MeanFlow can function as codecs inside the same reverse channel coding framework that DiffC uses for diffusion models. It derives the required posterior and shared distribution parameters from the models' existing velocity or noise parameterizations, using an equivalence for the flow-based models and local Gaussian approximations for CTM. The resulting formulation allows pre-trained few-step models to perform compression directly, which cuts the number of steps needed for encoding and decoding. On low-resolution image benchmarks this produces faster runtimes and better perceptual quality at low bit rates compared with many-step baselines.

Core claim

Rectified Flow and MeanFlow supply the quantities demanded by reverse channel coding through the equivalence between velocity parameterization and denoising parameterization; CTM, distilled from EDM, supplies them through the EDM noise parameterization together with local Gaussian approximations of sender and shared distributions at intermediate states. This construction yields a probabilistic codec that reuses any pre-trained few-step model without additional training.

What carries the argument

Reverse channel coding framework supplied with velocity-to-denoising equivalence for flow models and local Gaussian approximations at intermediate states for CTM.

If this is right

  • Encoding and decoding each require only a few steps instead of dozens or hundreds.
  • No retraining of the generative model is needed to obtain a working compressor.
  • Image realism improves relative to multi-step methods in the low-bit-rate regime.
  • The same adaptation applies across Rectified Flow, MeanFlow, and CTM.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach could be tested on higher-resolution images to check whether the local approximations remain accurate.
  • Other distilled or few-step models might be plugged into the same reverse channel coding construction.
  • The resulting codecs could be combined with conventional entropy coders to reach higher compression ratios.

Load-bearing premise

The velocity equivalence and local Gaussian approximations supply the exact posterior and shared distribution parameters required by reverse channel coding.

What would settle it

Measuring whether the bit rates and reconstruction quality obtained from the derived parameters deviate substantially from those of a full multi-step diffusion codec on the same images.

Figures

Figures reproduced from arXiv: 2606.10450 by Fuma Kimishima, Jinjia Zhou.

Figure 1
Figure 1. Figure 1: Overview of the reconstruction processes for different methods. The blue lines represent the communication steps while the red lines denote the generative process to reconstruct the image. Blue and red dots indicate the latent variables at specific timesteps t. The gray lines illustrate the underlying trajectories learned by each generative model. While DiffC (left) requires multiple iterative steps to rec… view at source ↗
Figure 2
Figure 2. Figure 2: Rate–distortion and rate–realism curves, with distortion (PSNR and LPIPS) and realism (FID), plotted against bits per pixel (bpp). The top row shows results on CIFAR10, and the bottom row shows results on ImageNet 64 × 64 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Reconstructed images on the CIFAR10 at various PSNR and bpp. For DiffC, UQDM, CTMC, and MeFC, PSNR/bpp values are selected to enable a comparative analysis of their performance evaluation. In contrast, DiffC (RF) and ReFC are chosen from approximately the same bpp for direct comparison. ods at higher rates. ReFC improves over DiffC (RF), but remains weaker than CTMC and MeFC. In the rate-realism curves, CT… view at source ↗
Figure 4
Figure 4. Figure 4: Reconstructed images on ImageNet 64 × 64 dataset at various PSNR/bpp. Results are approximately aligned to match the bpp of UQDM [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Visualization of MeFC reconstructions on CIFAR10 from different time steps t. For small t (up to t = 3), reconstructions may differ from the input but remain perceptually plausible; for larger t, the decoder increasingly reconstructs the input with added Gaussian noise, which is then gradually removed. C. Details of DiffC (RF) To apply Rectified Flow models (e.g., Flux (Labs et al., 2025)) within the DiffC… view at source ↗
Figure 6
Figure 6. Figure 6: Reconstructed image comparison by changing the number of forward steps T. The top two rows show results for ImageNet 64×64, while the bottom two rows show results for ImageNet 256×256, which have been scaled to 64×64 resolutions for easier viewing [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Visual comparison results of varying the reconstructed methods for ReFC and MeFC on ImageNet 64×64. The displayed results show the reconstructed images from each timestep t over N steps. For ReFC, Euler method was applied with N = 1, 4, 20. When t ≤ N, the reconstruction performed over t steps. ReFC (Denoise) refers to a reconstruction method that employs ϵ-prediction with ϵ RF θ such like DDPM. CTMC also … view at source ↗
Figure 8
Figure 8. Figure 8: Reconstructed image comparison by changing the reconstruction steps on ImageNet 256×256. For MeFC, Euler method is applied for N = 4, 10 and in the case of N = 1, average velocity field u MF θ is used for one-step generation such as MeanFlow. ReFC applies Euler method when N = 1, 4, 10 and ϵ-prediction (ReFC (Denoise)). 18 [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Visual Comparison of each image compression method including JPEG, DiffC, DiffC (RF), UQDM, ReFC and CTMC, chosen at roughly same bpp. 19 [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Visual Comparison of image compression methods including JPEG, PerCo, DiffC, DiffC (RF), ReFC and MeFC on ImageNet 256×256. . 20 [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Visual Comparison of reconstructed images on ImageNet 256×256. We roughly choose the similar bpp. . 21 [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗
read the original abstract

DiffC provides a principled way to reuse pre-trained diffusion models for lossy compression, but its encoding and decoding procedures remain slow because they require many discretized forward and reverse steps. We study whether few-step generative models -- Rectified Flow, Consistency Trajectory Models (CTM), and MeanFlow -- can be cast as codecs within the same reverse channel coding (RCC) framework. The main challenge is that RCC requires posterior and shared distribution parameters, whereas these models do not explicitly parameterize intermediate conditional distributions. For Rectified Flow and MeanFlow, we use the equivalence between velocity parameterization and diffusion-style denoising parameterization to derive the quantities required by RCC. For CTM, which is distilled from EDM, we adopt the EDM noise parameterization together with local Gaussian approximations of the sender and shared distributions at intermediate states. This yields a proof-of-concept probabilistic formulation that enables compression with pre-trained few-step generative models without retraining. On low-resolution benchmarks, the resulting codecs reduce encoding and decoding time and improve realism in the low-bit-rate regime.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper extends the DiffC reverse channel coding (RCC) framework for lossy compression to few-step generative models (Rectified Flow, Consistency Trajectory Models (CTM), and MeanFlow). It derives the posterior and shared distribution parameters needed by RCC: via velocity-to-denoising reparameterization for Rectified Flow and MeanFlow, and via EDM noise parameterization plus local Gaussian approximations at intermediate states for CTM. The resulting codecs are evaluated on low-resolution benchmarks, where they reduce encoding/decoding time relative to multi-step DiffC and improve perceptual quality in the low-bit-rate regime, all without retraining the base models.

Significance. If the derived distributions satisfy the exact RCC requirements, the work supplies a practical route to fast, training-free compression codecs based on existing few-step models. The proof-of-concept nature and reported speed gains are potentially useful for deployment; however, the absence of explicit error bounds or quantitative checks on the approximations means the rate-distortion guarantees rest on unverified steps rather than on machine-checked derivations or reproducible parameter-free results.

major comments (3)
  1. [§3.2] §3.2 (CTM derivation): the local Gaussian approximation of sender and shared distributions at intermediate states is introduced without a bound on the approximation error or an empirical verification (e.g., measured KL divergence to the true conditional) that the resulting means and variances coincide with those demanded by the RCC construction; this directly affects whether the encoding/decoding procedure remains correct.
  2. [§3.1] §3.1 (Rectified Flow / MeanFlow): the velocity-to-denoising equivalence is invoked to obtain the RCC parameters, yet no explicit verification is supplied that the reparameterized conditional distributions are identical to the posterior and shared distributions required by the reverse channel coding theorem; any mismatch would invalidate the claimed probabilistic formulation.
  3. [§4 / Table 1] Experiments (Table 1 and §4): reported encoding/decoding times and perceptual metrics are given, but no ablation or sensitivity analysis quantifies how deviations from the exact RCC distributions affect achieved rate or distortion; without this, the empirical results do not confirm that the derived quantities satisfy the RCC requirements.
minor comments (2)
  1. [§3.2] Notation for the approximated variances in the CTM case is introduced without a clear mapping back to the EDM parameterization used in the base model.
  2. The abstract states that derivations are performed, yet the main text would benefit from a compact summary table listing the exact mean/variance expressions supplied to RCC for each model family.

Simulated Author's Rebuttal

3 responses · 0 unresolved

Thank you for the constructive feedback. We address each major comment below. Our work is a proof-of-concept showing that few-step models can be used for compression via the RCC framework; we commit to revisions that add the requested empirical checks and derivations to strengthen the presentation.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (CTM derivation): the local Gaussian approximation of sender and shared distributions at intermediate states is introduced without a bound on the approximation error or an empirical verification (e.g., measured KL divergence to the true conditional) that the resulting means and variances coincide with those demanded by the RCC construction; this directly affects whether the encoding/decoding procedure remains correct.

    Authors: We acknowledge that the local Gaussian approximation for CTM lacks an explicit error bound or verification in the current manuscript. The approximation is chosen because CTM trajectories are locally near-linear after distillation from EDM. In the revision we will add an empirical verification: we will sample trajectories, estimate the true conditional via Monte Carlo, and report the average KL divergence to the Gaussian approximation at several intermediate states. This will quantify how closely the means and variances match the RCC requirements. revision: yes

  2. Referee: [§3.1] §3.1 (Rectified Flow / MeanFlow): the velocity-to-denoising equivalence is invoked to obtain the RCC parameters, yet no explicit verification is supplied that the reparameterized conditional distributions are identical to the posterior and shared distributions required by the reverse channel coding theorem; any mismatch would invalidate the claimed probabilistic formulation.

    Authors: The velocity-to-denoising reparameterization for Rectified Flow and MeanFlow is an exact equivalence that preserves the underlying probability path; both describe the same ODE. We will add a short appendix derivation in the revision that explicitly shows the reparameterized conditionals are identical to the posterior and shared distributions required by the RCC theorem, confirming there is no mismatch. revision: yes

  3. Referee: [§4 / Table 1] Experiments (Table 1 and §4): reported encoding/decoding times and perceptual metrics are given, but no ablation or sensitivity analysis quantifies how deviations from the exact RCC distributions affect achieved rate or distortion; without this, the empirical results do not confirm that the derived quantities satisfy the RCC requirements.

    Authors: We agree that an ablation quantifying sensitivity to deviations from exact RCC parameters would strengthen the empirical claims. In the revised manuscript we will add a sensitivity study that perturbs the derived means/variances by small amounts and reports the resulting changes in rate and perceptual distortion on the same low-resolution benchmarks. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivations use external equivalences and explicit assumptions

full rationale

The paper's central step is to cast few-step models into the existing RCC framework by adopting velocity-to-denoising equivalences (for RF/MF) and EDM noise parameterization plus local Gaussian approximations (for CTM). These are presented as adoptions from prior literature and stated assumptions rather than quantities fitted or derived inside this work. No self-definitional reductions, fitted-input-as-prediction, or load-bearing self-citation chains appear; the probabilistic formulation is obtained by direct substitution of these external parameterizations into RCC, which remains falsifiable against the true conditionals.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The approach rests on two domain assumptions imported from prior generative-model papers and one modeling approximation introduced for CTM; no free parameters or new entities are declared in the abstract.

axioms (2)
  • domain assumption Equivalence between velocity parameterization and diffusion-style denoising parameterization holds for Rectified Flow and MeanFlow at the intermediate states needed by RCC
    Invoked to obtain the posterior and shared distribution parameters required by the compression framework
  • ad hoc to paper Local Gaussian approximations of sender and shared distributions are adequate for CTM at intermediate states
    Adopted because CTM does not explicitly parameterize the conditional distributions demanded by RCC

pith-pipeline@v0.9.1-grok · 5702 in / 1323 out tokens · 21694 ms · 2026-06-27T14:10:47.267133+00:00 · methodology

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Reference graph

Works this paper leans on

23 extracted references · 4 canonical work pages · 1 internal anchor

  1. [1]

    Ball´e, J., Laparra, V ., and Simoncelli, E. P. End-to- 8 Few-step Generative Models as Lossy Compression end optimized image compression.arXiv preprint arXiv:1611.01704,

    arXiv

  2. [2]

    J., and Johnston, N

    Ball´e, J., Minnen, D., Singh, S., Hwang, S. J., and Johnston, N. Variational image compression with a scale hyperprior. arXiv preprint arXiv:1802.01436,

    Pith/arXiv arXiv

  3. [3]

    ImageNet: A large- scale hierarchical image database

    doi: 10.1109/CVPR.2009.5206848. Flamich, G. Greedy poisson rejection sampling.Advances in Neural Information Processing Systems, 36:37089– 37127,

    work page doi:10.1109/cvpr.2009.5206848 2009

  4. [4]

    Z., and He, K

    Geng, Z., Deng, M., Bai, X., Kolter, J. Z., and He, K. Mean flows for one-step generative modeling.arXiv preprint arXiv:2505.13447,

    Pith/arXiv arXiv

  5. [5]

    High-fidelity image compres- sion with score-based generative models.arXiv preprint arXiv:2305.18231,

    Hoogeboom, E., Agustsson, E., Mentzer, F., Versari, L., Toderici, G., and Theis, L. High-fidelity image compres- sion with score-based generative models.arXiv preprint arXiv:2305.18231,

    arXiv

  6. [6]

    Consis- tency trajectory models: Learning probability flow ode trajectory of diffusion.arXiv preprint arXiv:2310.02279,

    Kim, D., Lai, C.-H., Liao, W.-H., Murata, N., Takida, Y ., Uesaka, T., He, Y ., Mitsufuji, Y ., and Ermon, S. Consis- tency trajectory models: Learning probability flow ode trajectory of diffusion.arXiv preprint arXiv:2310.02279,

    arXiv

  7. [7]

    Kingma, D. P. and Welling, M. Auto-encoding variational bayes.arXiv preprint arXiv:1312.6114,

    Pith/arXiv arXiv

  8. [8]

    Lai, C.-H., Song, Y ., Kim, D., Mitsufuji, Y ., and Ermon, S

    URLhttps://arxiv.org/abs/2506.15742. Lai, C.-H., Song, Y ., Kim, D., Mitsufuji, Y ., and Ermon, S. The principles of diffusion models.arXiv preprint arXiv:2510.21890,

    Pith/arXiv arXiv

  9. [9]

    Improving the training of rectified flows.arXiv preprint arXiv:2405.20320,

    Lee, S., Lin, Z., and Fanti, G. Improving the training of rectified flows.arXiv preprint arXiv:2405.20320,

    arXiv

  10. [10]

    T., Ben-Hamu, H., Nickel, M., and Le, M

    Lipman, Y ., Chen, R. T., Ben-Hamu, H., Nickel, M., and Le, M. Flow matching for generative modeling.arXiv preprint arXiv:2210.02747,

    Pith/arXiv arXiv

  11. [11]

    Flow straight and fast: Learning to generate and transfer data with rectified flow

    Liu, X., Gong, C., and Liu, Q. Flow straight and fast: Learning to generate and transfer data with rectified flow. arXiv preprint arXiv:2209.03003,

    Pith/arXiv arXiv

  12. [12]

    Com- pressed image generation with denoising diffusion code- book models.arXiv preprint arXiv:2502.01189,

    Ohayon, G., Manor, H., Michaeli, T., and Elad, M. Com- pressed image generation with denoising diffusion code- book models.arXiv preprint arXiv:2502.01189,

    arXiv

  13. [13]

    9 Few-step Generative Models as Lossy Compression Russakovsky, O., Deng, J., Su, H., Krause, J., Satheesh, S., Ma, S., Huang, Z., Karpathy, A., Khosla, A., Bernstein, M., Berg, A

    doi: 10.1109/TIT.1962.1057702. 9 Few-step Generative Models as Lossy Compression Russakovsky, O., Deng, J., Su, H., Krause, J., Satheesh, S., Ma, S., Huang, Z., Karpathy, A., Khosla, A., Bernstein, M., Berg, A. C., and Fei-Fei, L. ImageNet Large Scale Visual Recognition Challenge.International Journal of Computer Vision (IJCV), 115(3):211–252,

    work page doi:10.1109/tit.1962.1057702 1962

  14. [14]

    Score-Based Generative Modeling through Stochastic Differential Equations

    doi: 10.1007/s11263-015-0816-y. Song, Y ., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Er- mon, S., and Poole, B. Score-based generative modeling through stochastic differential equations.arXiv preprint arXiv:2011.13456,

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/s11263-015-0816-y 2011

  15. [15]

    Lossy image compression with compressive autoencoders

    Theis, L., Shi, W., Cunningham, A., and Husz ´ar, F. Lossy image compression with compressive autoencoders. arXiv preprint arXiv:1703.00395,

    Pith/arXiv arXiv

  16. [16]

    D., and Mentzer, F

    Theis, L., Salimans, T., Hoffman, M. D., and Mentzer, F. Lossy compression with gaussian diffusion.arXiv preprint arXiv:2206.08889,

    arXiv

  17. [17]

    and Liu, F

    V onderfecht, J. and Liu, F. Lossy compression with pretrained diffusion models.arXiv preprint arXiv:2501.09815,

    arXiv

  18. [18]

    C., and Mandt, S

    Yang, Y ., Will, J. C., and Mandt, S. Progressive compres- sion with universally quantized diffusion models.arXiv preprint arXiv:2412.10935,

    arXiv

  19. [19]

    Zhang, R., Isola, P., Efros, A

    doi: 10.1109/18.119699. Zhang, R., Isola, P., Efros, A. A., Shechtman, E., and Wang, O. The unreasonable effectiveness of deep features as a perceptual metric. InProceedings of the IEEE conference on computer vision and pattern recognition, pp. 586–595,

    work page doi:10.1109/18.119699

  20. [20]

    Py- Torch implementation of Mean Flows for One-step Gen- erative Modeling. 10 Few-step Generative Models as Lossy Compression Algorithm 3CalcMean Q Require:x t,x 0, αt, σt, αs, σs Ensure:µ t 1:µ t = αs(1−αt) σ2 t x0 + αt αs σ2 s σ2 t xt 2: Returnµ t 3: no operation Algorithm 4CalcMeanStd P Require:x t,ϵ θ, αt, σt, αs, σs Ensure:µ θ, ˜βt 1:µ θ = αs(1−αt) σ...

    2020

  21. [21]

    Notably, µθ can be expressed as a function of˜µt, which motivates the implementations ofCalcMean QandCalcMeanStd Pused in our codec

    and pθ(xt−1 |x t)) can be expressed by directly comparing the corresponding means˜µt andµ θ: Lt−1 =E q 1 2σ2 t ∥˜µt(xt,x 0)−µ θ(xt, t)∥2 +C(22) whereCis a constant value.µ θ(xt, t)can be represented with noise-prediction modelϵ θ: µθ(xt, t) =˜µ xt, 1p ¯αDDPM t xt − q 1−¯αDDPM t ϵθ(xt) ! = 1p αDDPM t xt − βtp 1−¯αDDPM t ϵθ(xt, t) ! (23) For a detailed deri...

    2020

  22. [22]

    In DiffC, the noise schedule parameters are αt = p ¯αDDPM t and σt = p 1−¯αDDPM t . B. Velocity–Noise Parameterization Equivalence for Flow Models In the continuous-time setting, the forward process is described by the SDE dxt =f(x t, t)dt+g(t)dw t,(24) where f(x t, t) is the drift coefficient, g(t) is the diffusion coefficient, and wt is a standard Wiene...

    2020

  23. [23]

    Following the velocity–noise parameterization equivalence discussed by Lai et al

    proposed the probability flow ODE (PF-ODE): dxt dt =f(x t, t)− 1 2 g(t)2∇x logp t(x).(27) The PF-ODE induces the same marginal distributions pt(x) as the reverse-time SDE, while enabling stable generation with deterministic numerical solvers. Following the velocity–noise parameterization equivalence discussed by Lai et al. (Lai et al., 2025), we summarize...

    2025