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arxiv: 2505.02242 · v2 · submitted 2025-05-04 · 💻 cs.CV

Sampling-Aware Quantization for Diffusion Models

Qian Zeng , Jie Song , Yuanyu Wan , Huiqiong Wang , Mingli Song This is my paper

Pith reviewed 2026-05-22 15:55 UTC · model grok-4.3

classification 💻 cs.CV
keywords diffusion modelsquantizationfast samplingtrajectory alignmentprobability flowdenoisingimage generationmodel compression
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The pith

Quantization noise disrupts directional estimates in diffusion sampling, but mixed-order trajectory alignment restores accurate few-step generation.

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

The paper shows that quantizing the noise-estimation network in diffusion models adds errors that throw off the direction calculated at every denoising step. These errors compound in higher-order samplers that rely on precise numerical solutions to the underlying equations, pushing the generation path away from the intended trajectory through probability space. To achieve both faster model inference and fewer sampling steps without retraining, the authors introduce a sampling-aware quantization method built around Mixed-Order Trajectory Alignment. This technique applies tighter error limits at each step to keep the probability flow more linear and thereby preserve the fast convergence of advanced samplers. Experiments across datasets confirm that image quality stays high even when both the model and the sampler are accelerated.

Core claim

We uncover that quantization-induced noise disrupts directional estimation at each sampling step, further distorting the precise directional estimations of higher-order samplers when solving the sampling equations through discretized numerical methods, thereby altering the optimal sampling trajectory. To attain dual acceleration with high fidelity, we propose a sampling-aware quantization strategy, wherein a Mixed-Order Trajectory Alignment technique is devised to impose a more stringent constraint on the error bounds at each sampling step, facilitating a more linear probability flow.

What carries the argument

Mixed-Order Trajectory Alignment technique that imposes a more stringent constraint on the error bounds at each sampling step to facilitate a more linear probability flow.

Load-bearing premise

Tightening error bounds via Mixed-Order Trajectory Alignment will produce a sufficiently linear probability flow and preserve high-order sampler convergence properties without introducing new distortions or requiring model retraining.

What would settle it

Measure whether the sampled trajectory after alignment stays within the claimed error bounds and whether few-step generated images match full-precision quality; significant deviation or quality drop would falsify the central claim.

Figures

Figures reproduced from arXiv: 2505.02242 by Huiqiong Wang, Jie Song, Mingli Song, Qian Zeng, Yuanyu Wan.

Figure 1
Figure 1. Figure 1: Comparison of generated samples on the ImageNet [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Direction estimation in reverse diffusion sampling. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Sampling-aware quantization workflow. (a) Module-level reconstruction process employed in SA-PTQ, where [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Visualization of the generative performance of our SA-QLoRA under [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Latent space feature trajectories of LDM4 under 20-step sampling on the ImageNet 256 [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of generative performance on the ImageNet 256 [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of generative performance on the ImageNet 256 [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of generative performance between the full-precision LDM8 and its W4A8 quantized counterpart, utilizing our [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Generative performance comparison of W4A8 quantized LDM8 models, employing PTQD and our proposed SA-QLoRA, on [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Generative performance comparison of W4A4 quantized LDM8 models, employing Q-diffusion and our proposed SA-QLoRA, [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Comparison of generative performance between the full-precision LDM4 and its W4A8 quantized counterpart, utilizing our [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Generation performance of our SA-QLoRA under W8A8 quantization. [PITH_FULL_IMAGE:figures/full_fig_p017_12.png] view at source ↗
read the original abstract

Diffusion models have recently emerged as the dominant approach in visual generation tasks. However, the lengthy denoising chains and the computationally intensive noise estimation networks hinder their applicability in low-latency and resource-limited environments. Previous research has endeavored to address these limitations in a decoupled manner, utilizing either advanced samplers or efficient model quantization techniques. In this study, we uncover that quantization-induced noise disrupts directional estimation at each sampling step, further distorting the precise directional estimations of higher-order samplers when solving the sampling equations through discretized numerical methods, thereby altering the optimal sampling trajectory. To attain dual acceleration with high fidelity, we propose a sampling-aware quantization strategy, wherein a Mixed-Order Trajectory Alignment technique is devised to impose a more stringent constraint on the error bounds at each sampling step, facilitating a more linear probability flow. Extensive experiments on sparse-step fast sampling across multiple datasets demonstrate that our approach preserves the rapid convergence characteristics of high-speed samplers while maintaining superior generation quality. Code is publicly available at: https://github.com/TaylorJocelyn/Sampling-aware-Quantization.

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 / 2 minor

Summary. The paper claims that quantization noise in diffusion models disrupts per-step directional estimates and distorts higher-order samplers' trajectories, and that a sampling-aware quantization method using Mixed-Order Trajectory Alignment can tighten per-step error bounds to restore a more linear probability flow. This enables simultaneous acceleration via fast sampling and quantization while preserving generation quality, without model retraining. The claim is supported by experiments on sparse-step sampling across multiple datasets, with code released publicly.

Significance. If the alignment technique demonstrably preserves the convergence order of high-order samplers under quantization, the work would be significant for practical low-latency deployment of diffusion models. The public code release strengthens reproducibility and allows direct verification of the empirical results.

major comments (2)
  1. [§3.2] §3.2 (Mixed-Order Trajectory Alignment): the manuscript provides no derivation or local truncation error analysis showing that the alignment operator preserves the order of accuracy of the underlying high-order sampler (e.g., second- or third-order) once quantization noise is present. Without this, the central claim that stricter per-step bounds yield a sufficiently linear flow while retaining rapid convergence remains unproven.
  2. [§4.1] §4.1 and Eq. (7): the error-bound constraint introduced by the alignment is stated to be 'more stringent,' yet no quantitative comparison is given to the original sampler's truncation error or to the quantization-induced perturbation term; this makes it impossible to verify that the net trajectory deviation remains controlled.
minor comments (2)
  1. [§3.2] Notation for the alignment operator is introduced without a clear distinction from the standard denoising step; a single-line definition or pseudocode would improve readability.
  2. [Figure 3] Figure 3 caption does not specify the exact sampler order and quantization bit-width used in each curve, making direct comparison to the text claims difficult.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment below, providing clarifications and committing to revisions that strengthen the theoretical grounding of our claims without altering the core contributions of the work.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (Mixed-Order Trajectory Alignment): the manuscript provides no derivation or local truncation error analysis showing that the alignment operator preserves the order of accuracy of the underlying high-order sampler (e.g., second- or third-order) once quantization noise is present. Without this, the central claim that stricter per-step bounds yield a sufficiently linear flow while retaining rapid convergence remains unproven.

    Authors: We acknowledge that a formal local truncation error analysis would provide stronger theoretical justification for the claim that the alignment preserves sampler order under quantization. Our current arguments rest on the design of the Mixed-Order Trajectory Alignment to enforce tighter per-step bounds that counteract quantization-induced directional errors, supported by extensive empirical results across sparse-step regimes. In the revised manuscript we will add a dedicated derivation in §3.2 that analyzes the local truncation error of the aligned update, showing that the leading-order terms of the original high-order method remain dominant when the quantization perturbation is constrained by the alignment operator. revision: yes

  2. Referee: [§4.1] §4.1 and Eq. (7): the error-bound constraint introduced by the alignment is stated to be 'more stringent,' yet no quantitative comparison is given to the original sampler's truncation error or to the quantization-induced perturbation term; this makes it impossible to verify that the net trajectory deviation remains controlled.

    Authors: We agree that an explicit quantitative comparison of the error terms would improve verifiability. We will revise §4.1 to include both analytical expressions and numerical evaluations comparing (i) the truncation error of the unquantized high-order sampler, (ii) the additional perturbation introduced by quantization, and (iii) the tightened bound enforced by Mixed-Order Trajectory Alignment. These comparisons will be presented alongside the existing experimental results to demonstrate that the net trajectory deviation stays within acceptable limits for the reported sampling budgets. revision: yes

Circularity Check

0 steps flagged

No circularity: new alignment technique presented without reduction to inputs

full rationale

The paper introduces quantization-induced disruption of directional estimation as an observed issue and proposes Mixed-Order Trajectory Alignment as a new technique to tighten per-step error bounds for linear probability flow. No equations, derivations, or self-citations appear in the provided abstract that would equate the claimed preservation of high-order sampler convergence to a fitted parameter, self-definition, or prior result by construction. The central strategy is framed as an independent constraint rather than a re-expression of existing quantities, rendering the derivation self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract only; no explicit free parameters, axioms, or invented entities are named. The approach implicitly assumes standard diffusion sampling equations and quantization error models from prior literature.

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