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Hallucination-Aware Diffusion Sampling for Inverse Problems via Robust Prior Updates

Pengfei Jin, Yiqi Tian, Kailong Fan, Bingjie Qi, Quanzheng Li

arXiv:2606.02331v1cs.CVcs.LG

TL;DR

Diffusion inverse solvers can produce realistic reconstructions with details unsupported by their measurements, and the mechanisms by which such hallucinations enter remain an open question. The paper separates prior updates from measurement conditioning and proposes RPU to robustify the prior-side update. Its evaluations report improvements on FFHQ and human-preferred reconstructions, while broader evidence remains task dependent.

  • Problem

    Realistic diffusion reconstructions may contain meaningful details unsupported by the measurement, and how such hallucinations enter solvers remains insufficiently studied.

    Source: §1 · p. 2

  • Method

    RPU probes and re-anchors the prior-side update in a Bayes-rule-based solver while leaving the measurement condition unchanged.

    Source: §1 · p. 2, §5 · p. 8, §7 · p. 11

  • Results

    RPU improves PSNR and LPIPS across three FFHQ tasks, with reader studies showing instance-level faithfulness gains and ImageNet Gaussian results indicating transfer to a broader object distribution.

    Source: §7 · p. 11

  • Takeaways & Limitations

    The results support robust prior updates as a targeted intervention for more faithful diffusion inverse solvers, not as a replacement for reconstruction metrics or human inspection.

    Source: §7 · p. 11

    RPU is not a hallucination detector, and broader claims require more operators, datasets, reader populations, and integrations beyond the studied DPS instantiation.

    Source: §7 · p. 11

Abstract

from arXiv · show

Diffusion-based inverse problem solvers can produce realistic reconstructions, but realism alone does not ensure that the recovered details are supported by the measurement. We study this failure as measurement-conditioned hallucination: visually meaningful content that is either implausible or inconsistent with the measured instance. Our analysis separates Bayes-rule-based diffusion inverse solvers into a prior update and a measurement-conditioning step, showing that hallucinated content can enter through the prior-side proposal before the measurement correction is applied. Motivated by this view, we propose Robust Prior Update (RPU), a solver-level module that probes the local stability of the diffusion prior update, re-anchors the resulting displacement at the current iterate, and leaves the measurement update unchanged. We instantiate RPU in DPS and evaluate it on FFHQ and ImageNet inverse problems using automatic metrics and human faithfulness studies. On FFHQ, RPU improves PSNR and LPIPS over DPS across box inpainting, Gaussian deblurring, and motion deblurring. In human judgments, RPU receives 91.9% of blind non-tie majority preferences and 91.1% of ground-truth-assisted non-tie preferences on FFHQ box inpainting, while the ImageNet Gaussian reader study is tie-heavy but favors RPU among non-tie cases. These results support a targeted claim: robustifying the prior update can improve instance faithfulness in diffusion inverse solvers, especially when the prior shapes weakly constrained content.

1 Introduction

Diffusion priors can resolve ambiguity in inverse problems, yet realistic reconstructions may contain details unsupported by the measurement. The paper studies how such hallucinations enter diffusion solvers and proposes robustifying the prior update while leaving measurement conditioning fixed.

Motivation

  • Realistic reconstructions can contain meaningful details unsupported by the measurement, so visual plausibility alone does not establish instance faithfulness.This matters in conditional tasks such as medical imaging, where unsupported changes may affect interpretation, diagnosis, or downstream analysis.Source: §1 · p. 2
  • Relatively few studies examine how hallucination errors arise inside diffusion-based inverse solvers, leaving open when unsupported details enter and persist despite measurement corrections.Source: §1 · p. 2

Contributions

  • The paper distinguishes Type-I hallucinations—visually implausible artifacts—from Type-II hallucinations—plausible but measurement-unsupported details.Source: §1 · p. 2
  • An alternating-optimization view separates measurement consistency from the prior update and identifies the prior update as an intervention point.Source: §1 · p. 2
  • RPU stabilizes the prior-induced displacement while keeping the measurement update fixed.Source: §1 · p. 2
  • RPU is instantiated in DPS and evaluated with quantitative metrics and human faithfulness judgments on FFHQ and ImageNet inverse problems.Source: §1 · p. 2

2 Related Work

Related work spans diffusion inverse solvers, hallucination in generative and reconstruction settings, and perturbation-based robustness. This paper focuses on how prior-side proposals shape hallucination in Bayes-rule-based diffusion trajectories.

Diffusion-based inverse-problem solvers

  • Diffusion inverse solvers combine pretrained priors with measurement models through approaches including posterior guidance, variational or plug-and-play objectives, latent optimization, and Monte Carlo posterior sampling.The paper focuses especially on Bayes-rule-based solvers such as DPS.Source: §2 · pp. 2–3

Overview

  • Figure 1 depicts the solver’s balance between measurement fidelity and the diffusion prior, RPU’s prior-update intervention, and a Gaussian-deblurring example comparing DPS with RPU.The example identifies a partial eyeglass and unsupported mouth detail in DPS.Source: Figure 1 · p. 3

Hallucination in generative and reconstruction models

  • Conditional reconstruction can look plausible while containing structures unsupported by the observation; prior studies address this through null-space analysis, restoration limits, hallucination indexes, and mitigation.This paper instead examines how such content enters a Bayes-rule-based diffusion trajectory.Source: §2 · p. 3

Robust optimization and perturbation-based robustness

  • Robust optimization handles uncertainty through worst-case perturbations, while related machine-learning methods use adversarial training and perturbation-based regularization for local stability.The paper applies this perspective at the sampler level to the prior-side update.Source: §2 · p. 3

3 Preliminary and Hallucination Definition

The preliminaries frame inverse solving as combining measurement consistency with a prior, and describe Bayes-rule-based diffusion solvers through prior and measurement-matching directions. The section defines hallucination as solver-induced meaningful content unfaithful to the measured instance, distinguishing it from ordinary reconstruction error.

3.1 Diffusion-based inverse problem solver

  • For Gaussian measurement noise, the measurement-consistency term is f(x; y, A) = 1/(2σ_y^2) ||A(x) − y||^2; a standard reconstruction objective balances f with an image prior g.Source: §3.1 · p. 4
  • Bayes-rule-based diffusion solvers decompose posterior guidance into a diffusion-score direction and a measurement-matching direction; DPS approximates the latter using a denoised estimate.The diffusion prior is written as g_σ(x) = λϕ_σ(x), where ϕ_σ(x) = −log p_σ(x).Source: §3.1 · p. 4

3.2 Hallucination Definition

  • Inverse-problem hallucination is meaningful content introduced or substantially amplified by reconstruction that is unfaithful to the ground-truth instance under the measurement model.Type-I denotes visible artifacts or unstable structures; Type-II denotes plausible-looking details inconsistent with the ground truth.Source: §3.2 · p. 4
  • Blurring, missing texture, and small pixel deviations may lower reconstruction quality without necessarily constituting hallucination.Source: §3.2 · p. 4

4 Alternating Optimization View

The section frames Bayes-rule-based diffusion inverse solvers as combining measurement matching with a diffusion-prior update, and uses this split to analyze their updates locally. It connects that view to posterior-score solvers, including DPS.

4.1 Continuation alternating subproblems

  • The measurement and prior terms are modeled as local proximal subproblems; exact or approximate oracles allow different solvers, and a one-step first-order approximation yields the split update.The proximal terms make each subproblem a local correction around the current iterate rather than an isolated minimization.Source: §4.1 · p. 5

4.2 Local fixed-smoothing analysis

  • Under local regularity and positive step coefficients, the split update has fixed-σ descent; a local Polyak–Lojasiewicz condition further yields contraction.These are local fixed-smoothing guarantees, not a global convergence theorem for diffusion sampling.Source: §4.2 · pp. 5–6
  • A sufficiently slow decreasing-σ schedule tracks overlapping local basins to a stationary point of F0, provided the stated local assumptions hold.The schedule smooths the prior landscape at larger σ and sharpens it toward the target prior as σ decreases.Source: §4.2 · pp. 5–6

4.3 Correspondence to Bayes-rule solvers

  • The conditional score separates prior and likelihood directions; DPS [22] uses a denoised surrogate for measurement correction, while the prior fills structure weakly constrained by the measurement.This correspondence motivates keeping the measurement oracle fixed while robustifying the prior oracle.Source: §4.3 · p. 6

5 RPU: Robust Prior Update

RPU probes the local stability of the diffusion prior update and re-anchors its displacement at the current iterate. It changes the prior-side proposal while leaving DPS measurement correction unchanged.

5 RPU: Robust Prior Update

  • RPU probes local prior stability by stepping against the normalized prior displacement; the probe count K and radius γ_t set the perturbation, whose scale follows native reverse-step variance.The perturbed point is used to evaluate local prior behavior, not as a replacement for the current iterate.Source: §5 · p. 7
  • RPU evaluates the prior at the probed point but transfers only its resulting displacement to the original iterate, keeping the reverse trajectory anchored before measurement conditioning.This re-anchoring distinguishes the method from directly perturbing the sample.Source: §5 · p. 8
  • RPU changes the prior sample and the denoised estimate supplied to DPS, but leaves the measurement correction unchanged.The measurement operator, data-fidelity loss, and conditioning rule are also kept unchanged.Source: §5 · pp. 7–8

6 Experiments

The experiments evaluate RPU on FFHQ and ImageNet using reconstruction metrics and human faithfulness judgments. On FFHQ, RPU improves PSNR and LPIPS across three inverse problems, with the strongest reader preferences in box inpainting; ImageNet is treated as a transfer check.

6.1 Setup

  • FFHQ uses 1,000 images per degradation at 256 × 256 resolution across box inpainting, Gaussian deblurring, and motion deblurring; ImageNet Gaussian deblurring is a secondary transfer check.The main-text ImageNet setting uses 1,000 images at 256 × 256 resolution.Source: §6.1 · p. 8

6.2 Evaluation Metrics

  • PSNR and LPIPS assess instance-level reconstruction, while FID measures distribution-level realism; FID alone does not assess whether details agree with the ground truth.The evaluation also uses blind and with-GT human comparisons, decoded into method preferences or ties.Source: §6.2 · p. 8

6.3 Results

  • RPU raises PSNR from 19.72 to 20.40 and lowers LPIPS from 0.400 to 0.394 in FFHQ box inpainting; human majorities favor it 68–6 blind and 102–10 with-GT.FID changes from 45.44 to 50.35.Source: Table 1 · p. 9, Table 2 · p. 9, §6.3 · p. 9
  • In FFHQ Gaussian deblurring, RPU raises PSNR from 17.71 to 17.84 and lowers LPIPS from 0.462 to 0.455; with-GT majorities favor RPU 25–4.Blind judgments are mostly ties, with 7 RPU and 6 DPS majorities; FID changes from 33.54 to 36.61.Source: Table 1 · p. 9, Table 2 · p. 9, §6.3 · p. 9
  • In FFHQ motion deblurring, RPU raises PSNR from 18.56 to 18.69 and lowers LPIPS from 0.440 to 0.436; with-GT majorities favor RPU 23–5.Blind judgments produce 994 ties; FID changes from 35.90 to 39.05.Source: Table 1 · p. 9, Table 2 · p. 9, §6.3 · p. 10
  • In FFHQ examples, RPU reduces measurement-inconsistent facial details and hallucinated structures relative to DPS while preserving comparable visual realism.Rows show motion deblurring, Gaussian deblurring, and box inpainting; columns show the corrupted input, DPS, RPU, and ground truth.Source: Figure 2 · p. 10
  • For ImageNet Gaussian deblurring, RPU raises PSNR from 20.406 to 20.509, while LPIPS changes from 0.5342 to 0.5491 and FID from 83.985 to 87.296.The with-GT study has 989 ties, 8 RPU wins, 3 DPS wins, and p = 0.2266.Source: Table 3 · p. 10, §6.3 · p. 10

7 Discussion, Limitations and Conclusion

The discussion locates hallucination in the split between the diffusion-prior proposal and measurement conditioning, and presents RPU as a targeted intervention on the prior update. FFHQ results support faithfulness gains, while the authors limit broader claims to the studied settings.

Discussion

  • RPU probes and re-anchors the prior-side update while leaving DPS measurement conditioning unchanged, isolating how generative content enters before measurement correction.The authors frame the prior proposal as the intervention point in Bayes-rule-based solvers.Source: §7 · p. 11
  • Across FFHQ box inpainting, Gaussian deblurring, and motion deblurring, RPU improves PSNR and LPIPS, while reader studies show instance-level gains not captured by automatic metrics alone.The ImageNet Gaussian experiment indicates transfer to a broader object distribution; the authors position RPU as a targeted faithfulness intervention, not a replacement for metrics or human inspection.Source: §7 · p. 11

Limitations

  • The empirical evidence is task dependent: box inpainting is strongly underconstrained, whereas blur tasks and ImageNet produce many reader-study ties.Broader claims require more operators, datasets, reader populations, and integrations beyond the DPS instantiation studied here; RPU does not label individual reconstructions as hallucinated.Source: §7 · p. 11

Conclusion

  • The conclusion characterizes RPU as robustifying the prior update while keeping measurement conditioning fixed, with the DPS instantiation improving FFHQ metrics and producing human-preferred reconstructions.The authors describe robust prior updates as a practical path toward more faithful diffusion inverse solvers.Source: §7 · p. 11

A Proofs and Details for Section 4

The appendix proof develops a local descent argument for split updates and then states conditions under which continuation tracks local stationary regions as smoothing decreases.

A.1 Proof of Proposition 1

  • The proof combines descent-lemma bounds for f and g across the split update's displacements to establish the stated inequality.It considers the split update and applies bounds across both the shared displacement and the prior step.Source: §A.1 · p. 15
  • The proof's contraction claim invokes a local PL inequality for F.The supplied proof passage introduces this condition as part of the contraction argument.Source: §A.1 · p. 15

A.2 Continuation tracking conditions

  • With overlapping consecutive basins, suitable stage outputs, and controlled objective drift, continuation preserves fixed-σ descent up to summable drift and tracks local stationary regions.As σ decreases to zero, an accumulation point remaining in the tracked basin is stationary for differentiable F0; for nonsmooth F0 the stated conclusion is local limiting stationarity.Source: §A.2 · p. 16

C ImageNet results

ImageNet is presented as a secondary transfer check, with the main text focusing on Gaussian deblurring and additional task results documented in the appendix.

ImageNet results

  • Table 4 reports secondary ImageNet 256×256-1k results, with ground-truth-assisted reader-study counts labeled as RPU, DPS, and tie majorities when available.The table covers Gaussian deblurring, motion deblurring, and box inpainting; the main text reports Gaussian deblurring because it has the updated three-reader with-GT study.Source: Table 4 · p. 16, C ImageNet results · p. 16

D Reader Study Details

The reader-study appendix describes FFHQ protocols, preference decoding, and agreement statistics, alongside example reconstructions that complement aggregate results.

Reader-study protocols

  • Each FFHQ reader study contains 1,000 items and three readers, with blind comparisons hiding ground truth and with-GT comparisons showing it.Method identities are decoded using saved key files, and the reported audit found aligned keys for all six FFHQ studies.Source: D Reader Study Details · p. 16
  • In the blind rubric, readers see only the two reconstructions; scores 1 and 2 select a method, while scores 0 and 3 count as ties.The raw rating categories are preserved separately even though both tie scores decode to a tie preference.Source: Table 5 · p. 17, D Reader Study Details · p. 17
  • In the ground-truth-assisted rubric, panels show input, two reconstructions, and ground truth; scores 0, 3, and 4 decode as ties.The rubric retains raw categories to distinguish both-faithful, both-unfaithful-and-similar, and both-unfaithful-and-different cases.Source: Table 6 · p. 17, D Reader Study Details · p. 17

Preference decoding and statistical tests

  • Per-image reader scores are decoded into DPS, RPU, or tie preferences, and binomial tests and Wilson intervals use only non-tie majority cases.Raw score counts are reported separately so tie-heavy behavior remains visible.Source: D Reader Study Details · p. 17, Table 7 · p. 18

Agreement statistics

  • Fleiss’ kappa is highest for box inpainting with ground truth at κ = 0.747 and lower for blur tasks, where ties reduce informative preference cases.With-ground-truth kappas are 0.747, 0.484, and 0.455 for box inpainting, Gaussian blur, and motion blur, respectively.Source: D Reader Study Details · p. 17

Qualitative examples

  • The appendix includes FFHQ box-inpainting examples selected from unanimous RPU-preference cases and additional Gaussian or motion deblurring examples.The examples complement aggregate results and illustrate changed prior-side reconstructions under the same measurement condition as DPS.Source: Figure 4 · p. 19, Figure 5 · p. 20

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