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arxiv: 2605.19317 · v1 · pith:PLEXSAJKnew · submitted 2026-05-19 · 💻 cs.LG · cs.AI

Inference-Time Scaling in Diffusion Models through Iterative Partial Refinement

Taegu Kang , Jaesik Yoon , Sungjin Ahn This is my paper

Pith reviewed 2026-05-20 06:44 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords inference-time scalingdiffusion modelsiterative partial refinementglobal consistencyreasoning tasksSudokumixed-noise conditioningverifier-free scaling
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The pith

Iterative partial refinement improves global consistency in diffusion model samples by revising subsets with richer context and no external verifiers.

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

The paper introduces Iterative Partial Refinement to scale inference compute in diffusion models for tasks that need global constraint satisfaction. Starting from an initial sample, the method repeatedly re-noises selected regions and regenerates them while holding the rest fixed, letting the model correct early choices once more surrounding information is available. This matters for settings where reward models or verifiers are unavailable or unreliable, because the approach still raises performance on constrained reasoning problems. On MNIST Sudoku the share of fully valid solutions rises from 55.8 percent to 75.0 percent. A sympathetic reader sees a practical route to better samples that relies only on the diffusion model itself.

Core claim

Iterative Partial Refinement (IPR) is an inference-time scaling method for sequential diffusion models that requires no external verifier. From an already-generated sample, IPR re-noises a subset of regions and regenerates those regions conditioned on the fixed regions. The process lets the model revise earlier decisions under a richer context than existed during the original generation. On reasoning tasks that demand global consistency, the method produces more coherent outputs; for MNIST Sudoku the valid-solution rate increases from 55.8% to 75.0%.

What carries the argument

Iterative Partial Refinement: selectively re-noising and regenerating regions of an existing diffusion sample, conditioned on the unchanged regions, to enable iterative revision.

If this is right

  • Performance improves on reasoning tasks that require satisfying global constraints.
  • On MNIST Sudoku the valid solution rate rises from 55.8% to 75.0%.
  • More globally consistent samples are obtained without external verification or reward models.
  • Sequential diffusion models that already use region-wise mixed-noise conditioning gain a tailored scaling method.

Where Pith is reading between the lines

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

  • Inference-time partial revision may substitute for some of the gains normally sought by training larger models or adding verifiers.
  • The same re-noising loop could be tested on other constrained generation problems such as molecule design or route planning.
  • When a cheap verifier is occasionally available, interleaving IPR steps with verifier checks might compound the accuracy gains.

Load-bearing premise

Re-noising a subset of regions and regenerating them conditioned on the remaining regions enables the model to revise earlier decisions under a richer context than was available during the initial generation.

What would settle it

Applying Iterative Partial Refinement to MNIST Sudoku samples and finding that the valid-solution rate stays at or below the baseline 55.8% would show the refinement step does not reliably improve global consistency.

Figures

Figures reproduced from arXiv: 2605.19317 by Jaesik Yoon, Sungjin Ahn, Taegu Kang.

Figure 1
Figure 1. Figure 1: Overview of Iterative Partial Refinement (IPR). Starting from an initial sample x (0) , IPR iteratively refines the output by repeating three steps: (1) randomly selecting a subset M(r) of regions, (2) replacing them with random noise, and (3) regenerating them conditioned on the remaining regions via the learned conditional distribution pθ(xM(r) | x\M(r) ). After R iterations, the refined sample x (R) is … view at source ↗
Figure 2
Figure 2. Figure 2: Qualitative results across three benchmarks. (a) On MNIST Sudoku, IPR progressively corrects constraint-violating cells (red background), converging to a valid solution. (b) On Counting Polygons, IPR refines the generated digits to match the polygon count and vertex type (red: invalid, green: valid). (c) On Even Pixels, color regions become more uniform and balanced over iterations. Hyperparameters. Unless… view at source ↗
Figure 3
Figure 3. Figure 3: IPR on MNIST Sudoku. (a) Valid Sudoku rate improves consistently with IPR iterations on the HARD setting. (b) Recovery rate from corrupted grids with K initially swapped cell pairs, showing robustness even under severe corruption. 0 10 20 30 40 50 Refinement Iteration 0.150 0.175 0.200 0.225 0.250 0.275 0.300 Number Match Accuracy IPR (Ours) Baseline (SRMs) 0 10 20 30 40 50 Refinement Iteration 0.9875 0.99… view at source ↗
Figure 4
Figure 4. Figure 4: IPR on Counting Polygons. (Left) Number Match Accuracy improves as iterations in￾crease. (Right) Vertex Uniformity reaches 100% within 50 iterations. Results. As shown in [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: IPR on Even Pixels. Balance Accuracy (left) and color consistency measured by Satura￾tion/Value std (middle, right) both improve with IPR iterations. 4.5 ABLATION STUDY We conduct ablation studies on MNIST Sudoku (HARD setting) to analyze the key design choices of IPR. Results are shown in [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Ablation studies on IPR hyperparameters. Valid Sudoku rate (%) on MNIST Sudoku HARD setting. (a) Resampling ratio α = 0.25 performs best. (b) Fixed Noise performs comparably to random noise, while Fixed Region selection degrades performance. In contrast, Zhang et al. (2025a) (VFScale) aims for verifier-free test-time scaling by using the diffusion model’s intrinsic energy as an internal scoring signal. It … view at source ↗
Figure 7
Figure 7. Figure 7: Generated examples on MNIST Sudoku (HARD). Each column shows the generated image at a different IPR iteration, progressing from left to right. Red backgrounds indicate cells that violate Sudoku constraints; violations decrease as refinement progresses [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Generated examples on K-Corrupted Sudoku (K ∈ {1, 3, 5}). Each row corresponds to K = 1, 3, 5 from top to bottom. Each column shows the generated image at a different IPR itera￾tion, progressing from left to right. Red backgrounds indicate cells that violate Sudoku constraints; violations decrease as refinement progresses. 12 [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Generated examples on Counting Polygons. Each column shows the generated image at a different IPR iteration, progressing from left to right. The digit and polygon count converge to match the constraint [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Generated examples on Even Pixels. Each column shows the generated image at a dif￾ferent IPR iteration, progressing from left to right. Color regions become more uniform and balanced across iterations. C EXPERIMENT DETAILS C.1 SPATIAL REASONING MODELS We use SRMs (Wewer et al., 2025) as our sequential diffusion backbone for inference. We use the pretrained models provided by the authors. Checkpoints were … view at source ↗
read the original abstract

Inference-time scaling has emerged as a major approach for improving reasoning capabilities, and has been increasingly applied to diffusion models. However, existing inference-time scaling methods for diffusion models typically rely on external verifiers or reward models to rank and select samples, limiting their scalability to settings where such evaluators are available and reliable. Moreover, while recent diffusion models perform sequential inference with region-wise, mixed-noise conditioning, inference-time scaling tailored to this setting remains relatively underexplored. We propose Iterative Partial Refinement (IPR), an inference-time scaling method for sequential diffusion that requires no external verifier. Starting from an already-generated sample, IPR re-noises a subset of regions and regenerates them conditioned on the remaining regions, enabling the model to revise earlier decisions under a richer context than was available during the initial generation. This iterative partial refinement produces more globally consistent samples without external verification. On reasoning tasks requiring global constraint satisfaction, IPR consistently improves performance: on MNIST Sudoku, the valid solution rate increases from 55.8% to 75.0%. These results show that iterative partial refinement alone can serve as an effective inference-time scaling strategy for diffusion models in sequential, mixed-noise settings. Code is available at: https://github.com/ahn-ml/IPR

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 proposes Iterative Partial Refinement (IPR), an inference-time scaling method for diffusion models operating in sequential, mixed-noise conditioning regimes. IPR begins with a generated sample, selects and re-noises subsets of regions, then regenerates those regions conditioned on the fixed remaining regions. This process is iterated to enable revision of earlier decisions under richer context, yielding more globally consistent outputs without external verifiers or reward models. The central empirical claim is that IPR raises the valid-solution rate on MNIST Sudoku from 55.8% to 75.0% and produces analogous gains on other constraint-satisfaction reasoning tasks.

Significance. If the performance gains are shown to arise specifically from the partial-conditioning mechanism rather than from additional model evaluations, the result would be significant: it supplies a verifier-free inference-time scaling strategy tailored to the region-wise generation setting now common in diffusion models. The public release of code at https://github.com/ahn-ml/IPR is a clear strength that supports reproducibility.

major comments (2)
  1. [Experimental results on MNIST Sudoku] The headline result (55.8 % → 75.0 % valid Sudoku solutions) is reported without a compute-matched control that expends the identical number of additional forward passes while removing the partial-refinement aspect (e.g., full-image re-noising, repeated independent sampling, or extended diffusion trajectories). Because each IPR iteration consumes extra model evaluations, the observed lift could be reproduced by any procedure that simply increases inference budget; this control is load-bearing for the claim that “richer context” from partial conditioning is the operative mechanism. (Abstract and experimental results section)
  2. [Experimental evaluation] The paper does not report the number of independent runs, standard deviations, or statistical significance tests for the Sudoku improvement. Without these, it is impossible to assess whether the 19.2-point gain is robust or could be explained by sampling variance. (Experimental evaluation)
minor comments (2)
  1. The abstract states that IPR “consistently improves performance” on multiple reasoning tasks but supplies quantitative numbers only for MNIST Sudoku. Full tables or figures for the remaining tasks should be added.
  2. Baseline details (exact diffusion schedule, number of denoising steps in the initial generation, and how the 55.8 % figure was obtained) are not stated in the abstract and must appear explicitly in the experimental section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. The comments highlight important aspects of experimental rigor that we address below. We have revised the manuscript to incorporate additional controls and statistical reporting.

read point-by-point responses

  1. Referee: [Experimental results on MNIST Sudoku] The headline result (55.8 % → 75.0 % valid Sudoku solutions) is reported without a compute-matched control that expends the identical number of additional forward passes while removing the partial-refinement aspect (e.g., full-image re-noising, repeated independent sampling, or extended diffusion trajectories). Because each IPR iteration consumes extra model evaluations, the observed lift could be reproduced by any procedure that simply increases inference budget; this control is load-bearing for the claim that “richer context” from partial conditioning is the operative mechanism. (Abstract and experimental results section)

    Authors: We agree that a compute-matched control is necessary to isolate the contribution of partial conditioning from a simple increase in inference budget. In the revised manuscript we will add experiments that match the total number of forward passes used by IPR but remove the partial-refinement mechanism, specifically full-image re-noising and repeated independent sampling from scratch. These baselines will be reported alongside the original IPR results to demonstrate that the performance lift arises from the ability to revise earlier decisions under richer fixed-region context rather than from additional evaluations alone. revision: yes

  2. Referee: [Experimental evaluation] The paper does not report the number of independent runs, standard deviations, or statistical significance tests for the Sudoku improvement. Without these, it is impossible to assess whether the 19.2-point gain is robust or could be explained by sampling variance. (Experimental evaluation)

    Authors: We acknowledge the omission. The original results were obtained from multiple random seeds, but variance statistics were not included. In the revised experimental evaluation section we will report means and standard deviations across five independent runs and include a statistical significance test (paired t-test) comparing the baseline and IPR conditions to quantify the robustness of the observed improvement. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical method with independent experimental support

full rationale

The paper proposes Iterative Partial Refinement (IPR) as an inference-time scaling procedure for diffusion models in sequential mixed-noise settings. It describes starting from a generated sample, re-noising subsets of regions, and regenerating conditioned on the remainder to enable revision under richer context. Performance is demonstrated empirically on reasoning tasks, e.g., MNIST Sudoku valid solution rate rising from 55.8% to 75.0%. No equations, fitted parameters, self-citations, or derivation chain appear in the provided text that reduce the central claim to inputs by construction. The result is a self-contained empirical procedure evaluated against external benchmarks rather than a closed mathematical derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that partial re-noising and conditional regeneration can leverage richer context to improve global consistency in diffusion models.

axioms (1)
  • domain assumption The pretrained diffusion model can effectively use fixed regions as conditioning to revise noisy subsets and produce globally consistent outputs.
    This premise is required for the iterative refinement step to yield the reported performance gains.

pith-pipeline@v0.9.0 · 5751 in / 1144 out tokens · 50092 ms · 2026-05-20T06:44:52.007046+00:00 · methodology

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