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arxiv: 2603.04005 · v2 · pith:3YJCEH3Anew · submitted 2026-03-04 · 💻 cs.IT · cs.LG· math.IT

Training-Free Rate-Distortion-Perception Traversal With Diffusion

Yuhan Wang , Suzhi Bi , Ying-Jun Angela Zhang This is my paper

Pith reviewed 2026-05-25 07:13 UTC · model grok-4.3

classification 💻 cs.IT cs.LGmath.IT
keywords rate-distortion-perceptiondiffusion modelsreverse channel codingtraining-free compressionGaussian optimalityAWGN observationsperceptual qualityprobability flow ODE
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The pith

Pre-trained diffusion models enable training-free traversal across the full rate-distortion-perception surface.

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

The paper presents a framework that pairs a reverse channel coding module with a score-scaled probability flow ODE decoder drawn from pre-trained diffusion models. This combination lets users reach any desired operating point on the RDP surface by changing parameters instead of retraining a network. The work proves that the diffusion decoder is optimal for the distortion-perception tradeoff under additive white Gaussian noise observations and that the complete system attains the optimal RDP function when the source is Gaussian. A sympathetic reader would care because earlier neural compressors lock the tradeoff at one location and demand fresh training for every new balance of rate, distortion, and perception.

Core claim

The proposed diffusion decoder is optimal for the distortion-perception tradeoff under AWGN observations, and the overall framework with the RCC module achieves the optimal RDP function in the Gaussian case. The approach is training-free and uses pre-trained diffusion models to adaptively compress while balancing bitrate, fidelity, and perceptual quality.

What carries the argument

The reverse channel coding (RCC) module paired with a score-scaled probability flow ODE decoder derived from pre-trained diffusion models.

If this is right

  • Any point on the RDP surface becomes reachable by tuning the RCC rate and the ODE scaling parameter.
  • The same pre-trained diffusion model works for multiple operating points without retraining.
  • The framework supplies both a practical method and a proof of optimality for the Gaussian-AWGN setting.
  • Empirical tests on multiple datasets confirm that the method can navigate the ternary tradeoff.

Where Pith is reading between the lines

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

  • The same construction might be tested on non-Gaussian sources to measure how far the optimality extends beyond the proved case.
  • If the diffusion model already approximates the data distribution well, the method could eliminate the need to train separate compressors for different perception levels.
  • Practical performance under non-AWGN channels remains open and could be checked with controlled experiments.

Load-bearing premise

Pre-trained diffusion models are assumed to be sufficiently expressive and well-calibrated to serve as near-optimal decoders once the score-scaled ODE and RCC components are added.

What would settle it

A direct computation that shows the achieved RDP curve falls short of the known optimal RDP function for Gaussian sources observed through AWGN would disprove the optimality claim.

Figures

Figures reproduced from arXiv: 2603.04005 by Suzhi Bi, Ying-Jun Angela Zhang, Yuhan Wang.

Figure 1
Figure 1. Figure 1: The proposed framework to traverse the RDP function using pre-trained diffusion models. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Information-theoretical RDP function for scalar Gaussian source (dashed line) and achieved rate, MSE, [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Effect of controlling t and ρ on different metrics for the CIFAR-10 dataset. Distortion is quantified by MSE, and perception is measured by LPIPS and FID. 10 3 10 2 10 1 MSE 0.0 0.1 0.2 0.3 0.4 LPIPS MSE vs LPIPS for Selected Timesteps Ours t=10 (BPP=1.591) Ours t=20 (BPP=1.058) Ours t=30 (BPP=0.813) Ours t=50 (BPP=0.569) Ours t=80 (BPP=0.403) Ours t=99 (BPP=0.340) Ours t=200 (BPP=0.180) Ours t=296 (BPP=0.… view at source ↗
Figure 4
Figure 4. Figure 4: Rate-distortion-perception curves on the CIFAR-10 dataset. Distortion levels are quantified by MSE and [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: RDP tradeoff traversed by our proposed scheme on the Kodak and DIV2K datasets. We show the results [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Samples from HiFiC, CDC, and our proposed schemes with different [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: RDP curves on CIFAR-10 using different metrics. [PITH_FULL_IMAGE:figures/full_fig_p032_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Sample reconstructions on CIFAR-10 under varying [PITH_FULL_IMAGE:figures/full_fig_p033_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: RDP metrics under ρ = 1 for SD1.5/2.1/XL and Flux [PITH_FULL_IMAGE:figures/full_fig_p034_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Effect of controlling t and ρ on different metrics for the Kodak and DIV2K datasets. Stable Diffusion 2.1 and Flux depict different rate-distortion (R-D) and rate-perception (R-P) curves. 20.0 22.5 25.0 27.5 30.0 32.5 35.0 PSNR 0.0 0.1 0.2 0.3 0.4 0.5 LPIPS RDP Tradeoff (PSNR vs LPIPS) on Kodak and DIV2K Datasets SD-2.1, t=10 (BPP=0.125) SD-2.1, t=20 (BPP=0.096) SD-2.1, t=30 (BPP=0.080) SD-2.1, t=50 (BPP=… view at source ↗
Figure 11
Figure 11. Figure 11: RDP curves for Kodak and DIV2K using PSNR vs. LPIPS under SD2.1 and Flux. [PITH_FULL_IMAGE:figures/full_fig_p034_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: RDP curves for Kodak dataset using MSE vs. FID under SD2.1 and Flux. [PITH_FULL_IMAGE:figures/full_fig_p035_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Sample reconstructions on Kodak dataset under different [PITH_FULL_IMAGE:figures/full_fig_p036_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Sample reconstructions on DIV2K dataset under different [PITH_FULL_IMAGE:figures/full_fig_p036_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Sample reconstructions provided by Flux under different [PITH_FULL_IMAGE:figures/full_fig_p037_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Sample reconstructions with high resolution details under different [PITH_FULL_IMAGE:figures/full_fig_p038_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Sample reconstructions with high resolution details under different [PITH_FULL_IMAGE:figures/full_fig_p038_17.png] view at source ↗
read the original abstract

The rate-distortion-perception (RDP) tradeoff characterizes the fundamental limits of lossy compression by jointly considering bitrate, reconstruction fidelity, and perceptual quality. While recent neural compression methods have improved perceptual performance, they typically operate at fixed points on the RDP surface, requiring retraining to target different tradeoffs. In this work, we propose a training-free framework that leverages pre-trained diffusion models to traverse the entire RDP surface. Our approach integrates a reverse channel coding (RCC) module with a novel score-scaled probability flow ODE decoder. We theoretically prove that the proposed diffusion decoder is optimal for the distortion-perception tradeoff under AWGN observations and that the overall framework with the RCC module achieves the optimal RDP function in the Gaussian case. Empirical results across multiple datasets demonstrate the framework's flexibility and effectiveness in navigating the ternary RDP tradeoff using pre-trained diffusion models. Our results establish a practical and theoretically grounded approach to adaptive, perception-aware compression.

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

2 major / 1 minor

Summary. The manuscript proposes a training-free framework for traversing the rate-distortion-perception (RDP) surface in lossy compression. It integrates a reverse channel coding (RCC) module with a novel score-scaled probability flow ODE decoder built on pre-trained diffusion models. The central claims are that this decoder is optimal for the distortion-perception tradeoff under AWGN observations and that the full RCC-augmented framework attains the optimal RDP function when the source is Gaussian, with supporting empirical results on multiple datasets.

Significance. If the optimality proofs are rigorously established and the assumptions on the pre-trained models hold, the result would be significant: it supplies a practical, training-free method to achieve any point on the RDP surface by leveraging existing diffusion checkpoints, thereby connecting information-theoretic limits to generative modeling without task-specific retraining.

major comments (2)
  1. [Abstract] Abstract: the claim that the diffusion decoder is optimal for the distortion-perception tradeoff under AWGN observations is asserted without any derivation steps, explicit assumption list, or proof sketch. Because this optimality is load-bearing for the central contribution, the manuscript must supply the full argument (including how the score-scaled PF-ODE yields the optimal posterior) rather than a high-level statement.
  2. Theoretical claims (Gaussian case): the assertion that the RCC-augmented framework achieves the optimal RDP function requires that the pre-trained diffusion model supplies a score function that exactly matches the source distribution under the AWGN observation model. No argument is provided showing that a generic checkpoint (typically trained on ImageNet-scale data) satisfies the required score-matching condition when the source is an arbitrary Gaussian or when the channel deviates from the training distribution; any mismatch immediately voids the optimality derivation.
minor comments (1)
  1. The abstract refers to 'empirical results across multiple datasets' demonstrating flexibility but does not name the datasets, the quantitative RDP metrics reported, or the baselines used for comparison.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful reading and constructive feedback on the theoretical claims. We address the major comments point by point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that the diffusion decoder is optimal for the distortion-perception tradeoff under AWGN observations is asserted without any derivation steps, explicit assumption list, or proof sketch. Because this optimality is load-bearing for the central contribution, the manuscript must supply the full argument (including how the score-scaled PF-ODE yields the optimal posterior) rather than a high-level statement.

    Authors: We agree that the abstract presents the optimality claim at a high level. The full derivation, including the explicit assumptions and the steps showing how the score-scaled PF-ODE produces the optimal posterior under AWGN, appears in Section 3 of the manuscript. We will revise the abstract to incorporate a concise proof sketch and assumption list, and we will expand the introduction to preview the argument. revision: yes

  2. Referee: [—] Theoretical claims (Gaussian case): the assertion that the RCC-augmented framework achieves the optimal RDP function requires that the pre-trained diffusion model supplies a score function that exactly matches the source distribution under the AWGN observation model. No argument is provided showing that a generic checkpoint (typically trained on ImageNet-scale data) satisfies the required score-matching condition when the source is an arbitrary Gaussian or when the channel deviates from the training distribution; any mismatch immediately voids the optimality derivation.

    Authors: The Gaussian-case optimality result is derived under the assumption that the diffusion model supplies an exact score match to the source under the AWGN observation model; we will add an explicit statement of this assumption in the revised manuscript. We do not provide (and cannot provide) an argument that a generic ImageNet-trained checkpoint satisfies exact score matching for an arbitrary Gaussian source or mismatched channel, as this would generally not hold. The theoretical claim is therefore conditional on the score-matching condition, while the empirical results demonstrate practical RDP traversal with approximate scores from existing checkpoints. revision: partial

standing simulated objections not resolved
  • We cannot supply an argument showing that generic pre-trained checkpoints satisfy the exact score-matching condition required for optimality when the source is an arbitrary Gaussian or the channel deviates from the training distribution.

Circularity Check

0 steps flagged

Theoretical optimality proof does not reduce to self-defined inputs or fitted quantities.

full rationale

The paper states a theoretical proof that the score-scaled probability flow ODE decoder is optimal for the distortion-perception tradeoff under AWGN observations and that the RCC-augmented framework attains the optimal RDP function for Gaussian sources. No equations, fitting procedures, or self-citation chains are visible that would make the optimality claim equivalent to its own inputs by construction. The result is presented as holding under explicit assumptions (AWGN channel, Gaussian source, sufficiently expressive pre-trained diffusion model) rather than being forced by redefinition or parameter fitting within the paper itself. This is the most common honest outcome for a derivation-focused theoretical claim.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on the existence of pre-trained diffusion models that can be repurposed via the new decoder and on the validity of the AWGN/Gaussian optimality conditions; no free parameters or invented entities beyond the decoder itself are mentioned.

axioms (2)
  • domain assumption The diffusion decoder is optimal for distortion-perception tradeoff under AWGN observations
    Stated as a proved result in the abstract; the proof is not supplied here.
  • domain assumption The full framework achieves the optimal RDP function for Gaussian sources
    Stated as a proved result in the abstract; the proof is not supplied here.
invented entities (1)
  • score-scaled probability flow ODE decoder no independent evidence
    purpose: To realize the optimal distortion-perception operating point inside the diffusion framework
    Introduced as the novel component that enables the claimed optimality.

pith-pipeline@v0.9.0 · 5692 in / 1461 out tokens · 35558 ms · 2026-05-25T07:13:37.695785+00:00 · methodology

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Reference graph

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