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arxiv: 2605.31596 · v1 · pith:OKQ4DZM5new · submitted 2026-05-29 · 💻 cs.CV · cs.LG

KLIP: localized distribution shift detection via KL-divergence with diffusion priors in Inverse Problems

Alireza Kheirandish , Jihoon Hong , Sara Fridovich-Keil This is my paper

Pith reviewed 2026-06-28 23:03 UTC · model grok-4.3

classification 💻 cs.CV cs.LG
keywords KL divergencediffusion modelsout-of-distribution detectioninverse problemslocalized detectioncomputational imagingmedical imaging
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The pith

A KL-divergence metric between diffusion prior and posterior detects and localizes distribution shifts in inverse problems without calibration data.

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

The paper establishes a method to detect out-of-distribution samples in inverse problems by measuring the Kullback-Leibler divergence between a diffusion model's prior distribution over clean images and the posterior distribution conditioned on the available measurements. This metric requires no calibration examples and no knowledge of what the shifted distribution looks like, yet it can flag an entire image as anomalous or highlight specific patches inside it. A sympathetic reader would care because inverse problems arise in medical imaging, astronomy, and other settings where only indirect measurements exist and where even small, localized shifts can matter. The approach is shown to catch subtle changes such as the appearance of tumors in liver CT scans and to work across multiple diffusion models and problem types.

Core claim

The authors introduce a metric that quantifies distribution shift by computing the KL divergence between the diffusion prior and the posterior distribution obtained while solving an inverse problem. This metric operates without requiring calibration data or knowledge of the shifted distribution. It supports detection at both the whole-image level and the localized patch level. Experiments demonstrate its ability to identify subtle shifts, such as the presence of tumors in liver CT scans, and its applicability across different diffusion models, datasets, and inverse problem types.

What carries the argument

The KLIP metric, defined as the Kullback-Leibler divergence between the diffusion prior and the posterior distribution.

If this is right

  • The metric enables OOD detection in inverse problems without any examples from the shifted distribution.
  • It supports localization of anomalous regions inside an image rather than only whole-image decisions.
  • It identifies subtle semantic shifts such as healthy versus tumor-containing medical scans.
  • The same construction applies across multiple diffusion models, datasets, and inverse-problem formulations.

Where Pith is reading between the lines

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

  • The localization output could be used inside iterative reconstruction loops to down-weight or mask suspect regions automatically.
  • Similar divergence checks might be tested with other generative priors once those priors are shown to be sufficiently accurate.
  • The method suggests a route to unsupervised quality control for any measurement-based imaging pipeline where a strong generative model is already available.

Load-bearing premise

The diffusion model must accurately represent the true underlying data distribution so that the KL divergence reliably signals distribution shift rather than mismatch between the model and reality.

What would settle it

If the metric fails to flag images containing tumors when the diffusion model was trained only on healthy scans, or if it consistently flags normal images as out-of-distribution, the central claim would be falsified.

Figures

Figures reproduced from arXiv: 2605.31596 by Alireza Kheirandish, Jihoon Hong, Sara Fridovich-Keil.

Figure 1
Figure 1. Figure 1: KLIP (middle row) is able to identify the precise loca￾tions of local distribution shifts from diffusion model samples ac￾quired through posterior sampling in an inverse problem (here, un￾derdetermined CT and Gaussian deblurring). The diffusion model is trained on only ID images (healthy CT scans and celebrity faces), and KLIP has no access to other OOD examples. ous OOD detection metrics are often based o… view at source ↗
Figure 2
Figure 2. Figure 2: Solving inverse problems using posterior sampling with a diffusion model, for a Gaussian de-blurring example. (a) Forward model of gaussian blur. (b) Posterior sampling using a diffusion model to recover the signal from the measurement y following Equation (6). We can see from the yellow boxes highlighting the Terminator’s red eye that the score of the likelihood guides sampling to be consistent with y, es… view at source ↗
Figure 3
Figure 3. Figure 3: Motivation for block and timestep restriction: (a) An example ID image of a healthy liver CT scan (top) and corresponding OOD image with a localized synthetic star artifact (bottom). (b) Histogram of the prior–posterior KL divergence (Equation (11)) for ID images and OOD images, normalized to [0, 1]. The ID and OOD images are not well separated. (c) Histogram of the block restricted KL divergence over the … view at source ↗
Figure 4
Figure 4. Figure 4: Visualization of image-level OOD detection in sparse-view CT scans. Top: Images in the Tuning set and OOD set. Red boxes annotate the stars and tumors. Middle: Heatmaps of KLIP computed pixel-wise (i.e. DB = 1). Bottom: Heatmaps overlaid on images, to show localization. Columns A through D use a predictor-corrector based diffusion model, and columns E through H use a patch-based diffusion model. For each m… view at source ↗
Figure 5
Figure 5. Figure 5: Visual results for image-level OOD detection on human faces. Top: Samples of the OOD set containing different localized artifacts such as scars. Middle: Heatmaps of KLIP computed pixel-wise (i.e. DB = 1). Bottom: Heatmaps overlaid on images, to show localization. Columns A through E are images from the CelebA test set with synthetically-added scars; columns F through H are images from film and television o… view at source ↗
Figure 6
Figure 6. Figure 6: Effect of different timestep ranges on KLIP. (A) Original images before Gaussian blur is applied. (B-F) KLIP heatmaps for timestep windows of length 0.1, [t0, t0 + 0.1], where t0 starts at 0 in (B) and is incrementally increased in steps of 0.1 up to 0.4. (G) KLIP heatmap for the window t ∈ [0.5, 1.0]. (H) KLIP heatmap for the window t ∈ [0.15, 0.35], which was tuned to optimize detection of star artifacts… view at source ↗
Figure 7
Figure 7. Figure 7: Sample images included in the ID and different OOD sets. Each row represents a distinct dataset, and each column shows 7 different samples from that dataset. From the top, we have (1) the ID set consisted of healthy CT scans from the CHAOS [18] evaluation dataset, (2) the OOD set with a star shaped artifact, used for hyperparameter tuning, and (3) 6 OOD sets containing synthetic liver tumors of different d… view at source ↗
Figure 8
Figure 8. Figure 8: Left of the dotted line: KLIP heatmaps. Top: forward [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Visual results for image-level OOD detection on sparse-view CT scans. Row 1: Images in the OOD set with synthetic star artifacts. Red boxes annotate where the stars are. Rows 2-4: Heatmaps of CutPaste [22], SimpleNet [24], and KLIP overlaid on images [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Visual results for image-level OOD detection on sparse-view CT scans. Row 1: Images in the OOD set with dark and large tumors. Red boxes annotate where the tumors are. Rows 2-4: Heatmaps of CutPaste [22], SimpleNet [24], and KLIP overlaid on images. 6 [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Visual results for image-level OOD detection on sparse-view CT scans. Row 1: Images in the OOD set with dark and small tumors. Red boxes annotate where the tumors are. Rows 2-4: Heatmaps of CutPaste [22], SimpleNet [24], and KLIP overlaid on images [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Visual results for image-level OOD detection on sparse-view CT scans. Row 1: Images in the OOD set with large tumors of medium darkness. Red boxes annotate where the tumors are. Rows 2-4: Heatmaps of CutPaste [22], SimpleNet [24], and KLIP overlaid on images. 7 [PITH_FULL_IMAGE:figures/full_fig_p017_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Visual results for image-level OOD detection on sparse-view CT scans. Row 1: Images in the OOD set with small tumors of medium darkness. Red boxes annotate where the tumors are. Rows 2-4: Heatmaps of CutPaste [22], SimpleNet [24], and KLIP overlaid on images [PITH_FULL_IMAGE:figures/full_fig_p018_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Visual results for image-level OOD detection on sparse-view CT scans. Row 1: Images in the OOD set with light and large tumors. Red boxes annotate where the tumors are. Rows 2-4: Heatmaps of CutPaste [22], SimpleNet [24], and KLIP overlaid on images. 8 [PITH_FULL_IMAGE:figures/full_fig_p018_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Visual results for image-level OOD detection on sparse-view CT scans. Row 1: Images in the OOD set with light and small tumors. Red boxes annotate where the tumors are. Rows 2-4: Heatmaps of CutPaste [22], SimpleNet [24], and KLIP overlaid on images. 9 [PITH_FULL_IMAGE:figures/full_fig_p019_15.png] view at source ↗
read the original abstract

Diffusion models have shown promising performance as data-driven priors for computational imaging, as well as some capacity to detect out-of-distribution (OOD) images. However, existing approaches to OOD detection often require some knowledge of the shifted distribution, fail to detect subtle or localized distribution shifts, and operate on full images, rather than the indirect measurements available in inverse problems. We propose an OOD detection metric based on the Kullback-Leibler divergence between the diffusion prior and the posterior distribution, that (i) does not require any calibration data or knowledge of the shifted distribution, and (ii) can detect whole images as OOD as well as localize OOD patches within an image. Experimentally, we show that this metric can detect subtle yet semantically meaningful distribution shifts, such as the shift from healthy liver CT scans to those with tumors, and generalizes across different types of diffusion models, datasets, and inverse problems. Our code can be found at https://github.com/voilalab/KLIP.

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 paper introduces KLIP, a method for detecting out-of-distribution (OOD) samples in inverse problems using the Kullback-Leibler divergence between a diffusion prior and the corresponding posterior distribution. It claims this approach requires no calibration data or knowledge of the shifted distribution, enables both global detection and localization of OOD patches, and generalizes across diffusion models, datasets, and inverse problems, as demonstrated on tasks like detecting tumors in liver CT scans.

Significance. If the central claim holds, this work would offer a calibration-free OOD detection tool tailored to diffusion-based inverse problem solvers, with the ability to localize shifts within images. This is particularly relevant for medical imaging applications where subtle shifts like pathological changes need to be detected. The public release of code is a positive aspect that supports reproducibility.

major comments (2)
  1. [Experiments] Experiments section: The paper does not include controlled ablation studies in which the diffusion prior is deliberately misspecified (e.g., trained on mismatched modality or lower-capacity model) while holding the inverse problem and distribution shift fixed; such tests are required to establish that the KL metric isolates shift rather than prior error, since the posterior is obtained via the same prior.
  2. [Method] Method section (KL metric definition): No error analysis, sensitivity bounds, or verification is provided showing that KL(prior || posterior) primarily reflects distribution shift instead of reconstruction artifacts induced by the measurement operator or the conditional sampling procedure itself.
minor comments (1)
  1. [Abstract] Abstract states experimental results but provides limited quantitative details; ensure all performance claims in the abstract are directly supported by specific numbers, tables, or figures in the main text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and constructive feedback on our work. We address each major comment below and outline the revisions we will make to the manuscript.

read point-by-point responses

  1. Referee: [Experiments] Experiments section: The paper does not include controlled ablation studies in which the diffusion prior is deliberately misspecified (e.g., trained on mismatched modality or lower-capacity model) while holding the inverse problem and distribution shift fixed; such tests are required to establish that the KL metric isolates shift rather than prior error, since the posterior is obtained via the same prior.

    Authors: We agree that controlled ablation studies with misspecified priors would provide stronger evidence that the KL divergence metric isolates the effect of distribution shift rather than errors in the prior itself. Our current experiments show that the approach generalizes across different diffusion models, which offers some support for robustness to prior variations. However, we will add the suggested controlled ablations in the revised manuscript, including cases with mismatched modalities and lower-capacity models, to directly address this concern. revision: yes

  2. Referee: [Method] Method section (KL metric definition): No error analysis, sensitivity bounds, or verification is provided showing that KL(prior || posterior) primarily reflects distribution shift instead of reconstruction artifacts induced by the measurement operator or the conditional sampling procedure itself.

    Authors: This is a valid point. The manuscript relies on empirical demonstrations across multiple inverse problems and distribution shifts to show the metric's effectiveness. To strengthen the theoretical grounding, we will include additional analysis and verification experiments that isolate the contribution of distribution shift from potential artifacts due to the measurement operator or sampling procedure in the revised version. revision: yes

Circularity Check

0 steps flagged

No circularity: metric defined directly from prior/posterior

full rationale

The paper defines the KLIP OOD metric explicitly as the Kullback-Leibler divergence between the diffusion prior p_θ(x) and the posterior p_θ(x|y) obtained via conditional sampling in the inverse-problem setting. This construction is direct and does not reduce to a fitted parameter, self-referential definition, or load-bearing self-citation. No equations or claims in the abstract invoke uniqueness theorems, ansatzes smuggled via prior work, or renaming of known results; the central claim remains independent of its own inputs. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that diffusion models are faithful priors; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption Diffusion models serve as effective data-driven priors for the distribution in inverse problems.
    The KL metric is defined using this prior; if the prior is inaccurate the divergence score loses meaning.

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discussion (0)

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