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REVIEW 4 major objections 7 minor 1 cited by

Lossy Compression with Pretrained Diffusion Models

T0 review · 4 major / 7 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Pretrained latent diffusion models can serve as complete zero-shot lossy image compressors: the first full implementation of the DiffC algorithm encodes images with Stable Diffusion in under 10 seconds and reaches rate-distortion curves…

desk verdict First working DiffC implementation on pretrained diffusion models, with a real evaluation weakness: the schedules are tuned on the very test images used for the rate-distortion curves. read the letter →

arxiv 2501.09815 v1 pith:EKZSKGHZ submitted 2025-01-16 cs.CV eess.IV

Jeremy Vonderfecht , Feng Liu This is my paper · ORCID
classification cs.CVeess.IV
keywords lossyimagecompressiondiffusionmodelsreverse-channelcodingPoissonfunctionalrepresentationrate-distortionzero-shotlatentgenerative
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that the DiffC algorithm—lossy compression by communicating a noised latent through a shared diffusion model's reverse process—can be fully implemented on top of pretrained latent diffusion models without any additional training. The authors introduce practical workarounds for reverse-channel coding, the step that had prevented DiffC from being completed, and demonstrate the first end-to-end implementation on Stable Diffusion 1.5, 2.1, XL, and Flux-dev. With these workarounds, encoding an image on Stable Diffusion 1.5 takes under 10 seconds, and the rate-distortion curves at low ultra-low bitrates are competitive with purpose-built generative codecs such as HiFiC, MS-ILLM, PerCo, and DiffEIC. If the claim holds, today's expensive pretrained diffusion models become reusable zero-shot image compressors whose bitrates improve as the models grow.

What carries the argument

The load-bearing object is the reverse-channel coding step inside the DiffC protocol. DiffC transmits a sequence of progressively denoised latents, sending each sample $x_t \sim q(x_t|x_{t+1}, x_0)$ using the receiver's shared model distribution $p_\theta(x_t|x_{t+1})$, which costs roughly $D_{\mathrm{KL}}(q\|p)$ bits per step; the receiver then denoises with probability-flow DDIM sampling to reconstruct the image. The paper makes this practical by exploiting the structure of the Gaussian posterior: when $D_{\mathrm{KL}}$ per step is too small for bitrate-efficient coding, it skips denoising steps; when too large, it splits the anisotropic Gaussian into independent chunks near a 16-bit sweet spot; and a custom GPU kernel implements the Poisson Functional Representation reverse-channel coder fast enough to make the overhead negligible. A greedy shortest-path optimization over the timestep schedule (Algorithm 3) selects the sequence of steps that minimizes expected bits.

What would settle it

Encode a held-out set of images that were not used to compute Algorithm 3's step schedule or the mean per-step DKL values, using the released protocol; if the rate-distortion curve drops noticeably relative to the reported Kodak/Div2K curves, the zero-shot claim overstates what users will see on new images.

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Extended reading notes

Core claim

The central claim is that the DiffC algorithm, previously analyzed only in idealized form, is practically implementable on pretrained latent diffusion models, and that these unmodified models are capable lossy image compressors. The paper's contribution is the first complete DiffC implementation, achieved by stepping over denoising stages when the per-step KL divergence is too small for efficient reverse-channel coding, splitting the high-dimensional Gaussian into independent chunks when the KL is too large, and using a fast custom reverse-channel coding kernel that makes the Poisson Functional Representation an acceptable overhead. The authors report that this practical implementation stays within about 30% of the bitrate of idealized reverse-channel coding at the same PSNR, compresses and decompresses with Stable Diffusion 1.5 in under 10 seconds, and produces rate-distortion and perceptual-quality curves competitive with state-of-the-art generative compression methods at low ultra-low bitrates, despite requiring no training and supporting any target bitrate progressively. Reconstruction fidelity is bounded by each latent diffusion model's autoencoder, with Flux's higher-fidelity VAE (32.4 dB PSNR on Kodak) allowing higher-quality compression than Stable Diffusion 1.5/2.1.

Load-bearing premise

The reported bitrates assume that the step schedule and per-step bit budgets, computed by averaging over the very Kodak and Div2K images used for evaluation, are a legitimate pre-established protocol that will perform the same on any new image.

Editorial extensions

If this is right

  • Any pretrained DDPM-class generative model can be turned into a lossy codec with no retraining, so improvements in generative modeling should transfer directly to compression performance.
  • DiffC is naturally progressive: a single encoder can target any bitrate by stopping the noising process at a chosen timestep, while trained codecs like PerCo or HiFiC need separate training per rate.
  • The measured gap between the practical and idealized rate-distortion curves quantifies what better reverse-channel coding would buy: closing that gap improves bitrate without any change to the diffusion model.
  • Flux's higher-fidelity autoencoder shifts DiffC into a higher-quality regime, remaining competitive with HiFiC near 0.46 bits per pixel, whereas Stable Diffusion 1.5/2.1 are best suited to ultra-low bitrates under about 25 dB PSNR.
  • Prompt conditioning did not pay for its bits on Stable Diffusion 1.5/2.1, and for SDXL and Flux it improved perceived quality but not distortion metrics.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: if the hard-coded DKL and timestep schedules are as robust as the appendix suggests, the same protocol could be ported to a new architecture by recomputing Algorithm 3 once on a small reference set, without per-image tuning.
  • Beyond the paper: the bitrate gap between the practical and idealized curves sets a concrete research target—a more efficient reverse-channel coder would immediately improve every DiffC codec with no retraining.
  • Beyond the paper: the same tricks of skipping small-KL steps and splitting Gaussian dimensions should transfer to audio or video latent diffusion models, where pretrained models exist but no DiffC implementation has been demonstrated.
  • Beyond the paper: the observation that hard-coded KL values below the true divergence cause little distortion suggests the protocol has a built-in robustness margin that a systematic sensitivity study could turn into a formal guarantee.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 7 minor

Summary. The paper presents DiffC, a full implementation of the diffusion-based lossy compression algorithm of Theis et al. (2022), applied zero-shot to pretrained Stable Diffusion 1.5, 2.1, XL, and Flux-dev. The authors contribute a fast CUDA implementation of Poisson functional representation (PFR) for reverse-channel coding, a greedy shortest-path algorithm for choosing denoising timestep schedules, and a hard-coded per-step DKL schedule intended to avoid side information. They report rate-distortion curves on Kodak and DIV2K against HiFiC, MS-ILLM, PerCo, and DiffEIC, and claim competitiveness at ultra-low bitrates, with SD1.5 encoding times under 10 seconds. The paper also adapts DiffC to flow-matching models by an SNR-preserving rescaling between OT-flow and DDPM timesteps.

Significance. If the claims hold, this is a valuable systems contribution: it is the first complete DiffC implementation, the public release includes a working CUDA RCC kernel, and the engineering removes a known bottleneck that had prevented full implementations. The conceptual framework is sound, and the paper honestly reports practical overheads and the fidelity limits imposed by the latent VAE. However, the central 'zero-shot' claim is currently too strong because both the timestep schedule and the per-step DKL values are derived from the very images used for evaluation. With a held-out schedule validation and a more precise baseline comparison, the method could become a strong training-free baseline for generative compression.

major comments (4)
  1. [§3.2, §3.5, Appendix A.5] Algorithm 3 takes as input X, the dataset of images to be encoded, and computes the timestep schedule by averaging per-step DKL over exactly those images; Appendix A.5 then hard-codes the per-step DKL schedule as the mean (or multiples of the mean) over the same Kodak/Div2K images. Consequently, the rate-distortion curves in Figure 2 are produced with schedules that have been fitted to the evaluation set, which does not demonstrate zero-shot performance for unseen images. The robustness experiment in Figure 5 varies the DKL schedule only around the dataset-mean value and therefore does not exclude a schedule-dependent bias that would appear with a schedule derived from an unrelated dataset. Please provide R-D curves using schedules fixed in advance from a held-out set (for example, computed on a different dataset or on a subset disjoint from the evaluation images) and report the resulting shift in PSNR, LPIPS, CLIP, and Q-Align at matched bitrates.
  2. [§4.2, Figure 2] The comparisons against HiFiC, MS-ILLM, PerCo, and DiffEIC do not state whether those baseline curves were recomputed with the same code and preprocessing, or taken from prior papers. If they are taken from prior publications, differences in evaluation protocol (Div2K subset selection, resizing or cropping, and the treatment of VAE reconstruction bounds) can bias the comparison. Please specify the origin of each baseline curve and, where feasible, evaluate the baselines on the identical preprocessed images used for DiffC.
  3. [Abstract and Table 1] The abstract claims the method is 'capable of compressing and decompressing images using Stable Diffusion in under 10 seconds,' but Table 1 reports SD1.5 encoding times up to 9.4 s and decoding times up to 8.5 s, so the combined encode-plus-decode time can exceed 18 s. If the claim refers to encoding alone, the wording should be corrected; if it refers to the full round trip, the claim is contradicted by the table. This should be clarified and the abstract adjusted accordingly.
  4. [§4.2, Figures 2 and 4] The R-D curves are shown without error bars or confidence intervals, but the encoding and decoding procedure is stochastic: PFR draws random samples, and the final reconstruction therefore varies across runs unless the random seeds are fixed. The paper does not state how many random trials were averaged, nor whether the plotted points are single runs. Without this information, the small differences between methods at matched bitrates are difficult to interpret. Please report the variance over PFR randomness, for example by encoding each image several times and showing standard errors.
minor comments (7)
  1. [§2.4] The notation 'Dkl' appears with inconsistent capitalization; please use a single consistent notation such as D_KL throughout, including in Section A.5.
  2. [§3 and §3.1] There are typographical errors: 'neglegible' should be 'negligible', and 'paralellism' should be 'parallelism'.
  3. [§3.2, Algorithm 3] Line 3 of Algorithm 3, 'Sample xT ∼ q(xT|x0) using p(xT)', is unclear: it should explain whether this is a direct sample from q that the receiver can reconstruct, or an RCC step, and how the receiver obtains the sample without side information.
  4. [§2.3, Equation (1)] The summation notation 'tX i=T' in the displayed formula is awkward and hard to read; please rewrite it as a standard sum over the relevant timestep indices.
  5. [§4.2 and Table 1] The dataset names are written inconsistently as 'Kodak', 'Div2K', and 'Div2k-1024'; please standardize the capitalization and the precise subset used for each curve.
  6. [§1] The cost figures for training Stable Diffusion are cited to Wikipedia, which is not an appropriate source for a research paper; please replace this citation with a primary source or remove the claim.
  7. [Figure 5 caption] The legend labels such as 'quarter mean' and 'twice mean' are ambiguous; please write 'one quarter of the mean' and 'twice the mean' for clarity.

Circularity Check

2 steps flagged · score 4.0 of 10

Timestep and per-step DKL schedules are optimized on the same Kodak/Div2K images later used for evaluation, so the reported zero-shot bitrates are in part fitted rather than predicted.

  1. fitted input called prediction [Section 3.2, Algorithm 3]
    "We optimize our timestep schedule for a set of images X: for the Kodak dataset, X consists of all 24 images. For Div2K we choose a random sample of 30 images. See Algorithm 3: ... C[i, j] ← mean(C(D[x, i, j]) for x ∈ X); S ← ShortestPath(C, T, tfinal)"

    Algorithm 3 takes the evaluation images themselves as X and returns the schedule S that minimizes the average coding cost over X. The rate-distortion curves in Figure 2 are then produced with this S on the same Kodak/Div2K images. By construction, the reported bitrate at each operating point is the minimum mean cost over the evaluated set under the chosen cost function, so it is a fitted quantity rather than the cost a zero-shot user would achieve on unseen images with a pre-existing schedule.

  2. fitted input called prediction [Section 3.5 / Appendix A.5]
    "To choose the hard-coded sequence of DKL values, we first run DiffC for each image in our dataset while allowing Dkl per step to be determined by the actual value of DKL (q||p) at each step. Then, instead of using those dynamically generated values, we fix the DKL values to their mean values across all images."

    The per-step DKL values that both sender and receiver must pre-establish are the means computed over the same Kodak/Div2K images whose RD curves are later reported. The bitrate numbers therefore incorporate a side-information schedule fitted to the test set, so they do not demonstrate zero-shot behavior with a schedule chosen independently of the evaluation images. The robustness experiment in Figure 5 only varies the schedule as fixed multiples of this dataset mean, which does not remove the dependence on the test set.

full rationale

The core derivation is not circular: DiffC is imported from Theis et al. (2022) and PFR from Theis and Ahmed (2022), both external to the present authors, and the paper measures actual rate-distortion performance against external baselines. The main circularity-adjacent flaw is evaluative rather than definitional: both the timestep schedule (Algorithm 3) and the hard-coded per-step DKL sequence (Appendix A.5) are computed from the same images used to report the RD curves. This is a test-set-fitting issue, not an equation-level equivalence, and the central implementation claim still has independent content. However, the headline 'zero-shot competitive' claim is only partially supported because a held-out schedule would be required to know whether the reported bitrates transfer to unseen images. Score 4 reflects one fitted-input-called-prediction pattern affecting the measurement of the central claim without collapsing the derivation into its inputs.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central method rests on standard DDPM and reverse-channel coding results from prior work, plus three paper-specific choices: a dataset-tuned timestep schedule, a hard-coded DKL schedule, and an assumed DDPM/OT-flow equivalence. No new physical or mathematical entities are postulated. The main burden is that two of the free parameters are fitted to the evaluation data, which should be stated as a limitation.

free parameters (4)
  • Timestep schedule S (greedy shortest path) = e.g., up to 163 steps for SD1.5 on Kodak; varies by model and dataset.
    Algorithm 3 selects the schedule that minimizes expected coding cost, computed from KL divergences on the evaluation images themselves (all 24 Kodak, or 30 sampled Div2K). This is a free choice fitted to the data, not a parameter-free derivation.
  • Hard-coded per-step DKL schedule = mean, min, max, and multiples (0.25x, 0.5x, 2x, 4x) of the dataset-mean schedule.
    Appendix A.5 fixes the DKL used per step to dataset-derived values instead of encoding them as side information; the choice affects the measured bitrate and is tuned on the evaluation set.
  • PFR chunk size = 16 bits.
    The authors choose 16-bit chunks as the sweet spot between RCC time complexity (exponential in DKL) and bitrate overhead; this is a hand-selected hyperparameter.
  • Denoising schedule for DiffC-F = 50-step DDIM; reconstruction from t in [900, 800, ..., 100, 90, ..., 10].
    The final denoising step count and the grid of noisy timesteps used to sweep bitrate are choices made by the authors, not imposed by the algorithm.
assumptions (5)
  • standard math The DDPM reverse posterior q(xt-1|xt,x0) is Gaussian and the diffusion model approximates the reverse transition p_theta(xt-1|xt).
    Used throughout Section 2.3 and Section 3 to derive the DiffC coding costs C(i,j) and the KL formulas. This is standard DDPM theory from Ho et al. 2020.
  • standard math PFR (Algorithm 4, from Theis and Ahmed 2022) samples exactly from q using shared p at expected cost close to DKL(q||p).
    The entire practical method relies on this external reverse-channel coding result, stated in Section 2.4 and used in Algorithms 1 and 4.
  • domain assumption Communicated samples xt are statistically indistinguishable from q(xt|x0), so each coding step can be optimized greedily and independently of how xt was obtained.
    This assumption underlies the 'optimal substructure' claim and the shortest-path schedule optimizer in Section 3.2; if rejected, the schedule optimization argument collapses.
  • domain assumption An OT-flow model (Flux-dev) can be treated as a DDPM by matching signal-to-noise ratios and rescaling the input latent.
    Appendix A.3 gives the transformation but only matches the marginal SNR; it assumes the joint behavior of the Flow Matching forward process aligns with a DDPM forward process well enough for DiffC coding to remain valid.
  • ad hoc to paper A hard-coded per-step DKL schedule based on dataset averages can replace per-image side information without materially changing measured bitrate or decoded samples.
    Appendix A.5 establishes this empirically on the evaluation set; it is an ad hoc protocol choice specific to this paper rather than a general result.

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Cite this review

Pith. "Pith review of Lossy Compression with Pretrained Diffusion Models." pith.science (2026). https://pith.science/paper/EKZSKGHZ

@misc{pith2026250109815,
  author       = {Pith},
  title        = {Pith review of: Lossy Compression with Pretrained Diffusion Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EKZSKGHZ}},
  note         = {Machine review of arXiv:2501.09815}
}
read the original abstract

We apply the DiffC algorithm (Theis et al. 2022) to Stable Diffusion 1.5, 2.1, XL, and Flux-dev, and demonstrate that these pretrained models are remarkably capable lossy image compressors. A principled algorithm for lossy compression using pretrained diffusion models has been understood since at least Ho et al. 2020, but challenges in reverse-channel coding have prevented such algorithms from ever being fully implemented. We introduce simple workarounds that lead to the first complete implementation of DiffC, which is capable of compressing and decompressing images using Stable Diffusion in under 10 seconds. Despite requiring no additional training, our method is competitive with other state-of-the-art generative compression methods at low ultra-low bitrates.

Figures

Figures reproduced from arXiv: 2501.09815 by the authors.

Figure 1
Figure 1. Kodak images compressed using our method on Stable Diffusion 1.5, Text-Sketch [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Rate-distortion curves for generative compression methods across three sets of images. [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Visual comparison of generative compression methods. [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: RD curves on Kodak dataset vs. number of RCC steps. Legend shows encoding time per [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: R-D curves for Stable Diffusion 1.5 on the Kodak dataset with various ways to determine [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]
Figure 6
Figure 6. Figure 6: Rate-distortion curves for Stable Diffusion 2.1 and SDXL on Kodak vs. Div2k-1024 [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]
Figure 7
Figure 7. Figure 7: Rate-distortion curves for unconditional vs. prompt-guided reconstructions with SDXL [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]

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Forward citations

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

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    @esa (Ref

    \@ifxundefined[1] #1\@undefined \@firstoftwo \@secondoftwo \@ifnum[1] #1 \@firstoftwo \@secondoftwo \@ifx[1] #1 \@firstoftwo \@secondoftwo [2] @ #1 \@temptokena #2 #1 @ \@temptokena \@ifclassloaded agu2001 natbib The agu2001 class already includes natbib coding, so you should ...

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    \@lbibitem[] @bibitem@first@sw\@secondoftwo \@lbibitem[#1]#2 \@extra@b@citeb \@ifundefined br@#2\@extra@b@citeb \@namedef br@#2 \@nameuse br@#2\@extra@b@citeb \@ifundefined b@#2\@extra@b@citeb @num @parse #2 @tmp #1 NAT@b@open@#2 NAT@b@shut@#2 \@ifnum @merge>\@ne @bibitem@firs...

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    @open @close @open @close and [1] URL: #1 \@ifundefined chapter * \@mkboth \@ifxundefined @sectionbib * \@mkboth * \@mkboth\@gobbletwo \@ifclassloaded amsart * \@ifclassloaded amsbook * \@ifxundefined @heading @heading NAT@ctr thebibliography [1] @ \@biblabel @NAT@ctr \@bibset...

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.