🤖 machine learning

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

This paper introduces Robust Prior Update (RPU), a solver-level module that mitigates measurement-conditioned hallucinations in diffusion-based inverse problems by stabilizing the prior update step, thereby significantly improving instance faithfulness and reconstruction quality across various tasks.

Original authors: Pengfei Jin, Yiqi Tian, Kailong Fan, Bingjie Qi, Quanzheng Li

Published 2026-06-02

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Pengfei Jin, Yiqi Tian, Kailong Fan, Bingjie Qi, Quanzheng Li

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: The "Too Creative" Artist

Imagine you are trying to restore an old, damaged photograph. Some parts are missing (like a face covered by a scratch), or the image is blurry. You hire a very talented artist (a Diffusion Model) to fill in the missing pieces.

The artist is amazing at guessing what a face should look like based on millions of other faces they've seen. However, because they are so creative, they sometimes add details that weren't actually in the original photo.

The Problem: They might draw a pair of glasses on a person who wasn't wearing any, or change the shape of a mouth just because it "looks good."
The Paper's Term: This is called Hallucination. In this context, it's not just a mistake; it's the artist inventing facts that the evidence (the damaged photo) doesn't support.

The authors of this paper realized that while the artist is trying to be helpful, they are getting too confident in their guesses before checking the actual evidence.

The Two-Step Dance

The paper explains that these AI solvers work in a two-step dance to fix the image:

The "Guess" Step (Prior Update): The artist looks at the blurry image and says, "I think this should be a nose here." They make a bold guess based on their training.
The "Check" Step (Measurement Conditioning): The artist then looks at the actual damaged photo and says, "Wait, does my guess match the pixels I can see?" They adjust the image to fit the evidence.

The Flaw: The paper argues that the "Guess" step is where the trouble starts. The artist makes a wild guess (hallucinating a nose) before the "Check" step happens. Even when they try to correct it later, that invented detail often sticks around because the "Check" step isn't strong enough to erase the artist's confidence.

The Solution: RPU (The "Reality Check" Pause)

The authors propose a new module called RPU (Robust Prior Update). Think of RPU as a "pause button" or a "stability test" inserted right before the artist makes their big guess.

Here is how RPU works, using a Tightrope Walker analogy:

Without RPU: The artist (the walker) takes a giant leap forward based on a hunch. If they are wrong, they might fall off the tightrope (create a fake detail).
With RPU: Before the artist takes that big leap, they take a few tiny, cautious steps back and forth to test the ground.
- They ask: "If I move my foot this way, is the ground stable? Or is it shaky?"
- If the ground is shaky (meaning the guess is unstable or likely to be a hallucination), RPU says, "Don't take that big leap."
- Instead, it anchors the artist back to their current safe spot and only allows a small, safe movement.

Crucially: RPU does not change the "Check" step. It doesn't change how the AI looks at the damaged photo. It only changes how the AI makes its initial guess, making that guess more careful and less likely to invent fake details.

What They Found (The Results)

The team tested this new method (RPU) against the standard method (DPS) using faces (FFHQ dataset) and general images (ImageNet).

Better Accuracy: When they measured the results with math (PSNR and LPIPS scores), RPU produced clearer, more accurate images than the standard method.
Human Preference: They asked humans to look at the results without knowing which was which.
- The Result: Humans overwhelmingly preferred the RPU images.
- Why? In the standard method, the AI often added fake details (like a partial pair of glasses or a weird mouth shape) that looked realistic but were wrong. RPU avoided these inventions, keeping the image faithful to the original evidence.
The "Tie" Factor: In some cases, the differences were so subtle that humans couldn't tell them apart (a "tie"). However, whenever humans could tell a difference, they almost always picked RPU as the one that looked more like the true original.

The Bottom Line

The paper claims that by making the "guessing" part of the AI more stable and cautious (Robust Prior Update), we can stop the AI from "hallucinating" fake details.

Before: The AI guesses wildly, then tries to fix it, but fake details often survive.
After (with RPU): The AI checks its own stability before guessing, ensuring that what it adds is actually supported by the evidence.

The authors conclude that this is a targeted fix: it doesn't make the AI "smarter" at guessing; it makes it more faithful to the specific photo it is trying to restore.

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

1. Problem Definition

Diffusion-based inverse problem solvers are capable of generating realistic reconstructions from incomplete or corrupted measurements (e.g., inpainting, deblurring, MRI). However, the paper identifies a critical failure mode termed measurement-conditioned hallucination. Unlike unconditional generation failures (e.g., distorted anatomy), this specific failure occurs when a reconstruction appears visually plausible but contains details that are not supported by the observed measurement $y$ .

The authors distinguish two types of hallucination:

Type-I: Visually implausible artifacts or unstable structures.
Type-II: Plausible-looking details that are inconsistent with the ground truth $x^\star$ and unsupported by the measurement model.

Standard metrics (PSNR, LPIPS, FID) often fail to detect Type-II hallucinations because they measure distributional realism or pixel-level consistency rather than instance-level faithfulness to the specific ground truth. The core question addressed is: When and how do unsupported details enter the diffusion-based inverse solving process, and how can they be mitigated without compromising measurement consistency?

2. Methodology: Alternating Optimization and RPU

The paper reframes Bayes-rule-based diffusion inverse solvers (specifically DPS) as an alternating optimization process consisting of two distinct steps:

Prior Update: The diffusion prior proposes a displacement to fill in missing or ambiguous content.
Measurement Conditioning: A correction step anchors the reconstruction to the observed measurement $y$ and operator $A$ .

The authors hypothesize that hallucinations often enter during the prior update step, where the generative model proposes content that is weakly constrained by the measurement. To address this, they propose Robust Prior Update (RPU), a solver-level module that intervenes only in the prior update step while leaving the measurement conditioning unchanged.

The RPU Mechanism:

Probing: Before accepting the native prior displacement $d_\theta(x_t, t)$ proposed by the diffusion model, RPU performs a local stability probe. It moves a small distance against the normalized prior displacement for $K$ steps, creating a perturbed point $x_t^{adv}$ .
Re-anchoring: The diffusion prior is evaluated at this perturbed point $x_t^{adv}$ $x_{t}^{a d v}$ to obtain a new displacement. Crucially, this displacement is re-anchored to the original iterate $x_t$ $x_{t}$ rather than the perturbed point.
- Formula: $\tilde{x}_{t-1}^{prior} = x_t + (p_\theta(x_t^{adv}, t) - x_t^{adv})$ .
Measurement Correction: The standard measurement update is then applied using the denoised estimate derived from the probed model output.

This approach effectively stabilizes the generative proposal by ensuring the prior displacement is locally robust to small perturbations, reducing the injection of unsupported details before the measurement constraint is reapplied.

3. Key Contributions

Definition of Hallucination: The paper formally defines inverse-problem hallucination, separating it into Type-I (implausible) and Type-II (measurement-unsupported but plausible) cases.
Theoretical Decomposition: It derives an alternating-optimization view of Bayes-rule-based solvers, explicitly separating the measurement-consistency step from the prior-update step and identifying the prior update as the intervention point for hallucination.
RPU Algorithm: The proposal of RPU, a module that probes local stability of the prior update and re-anchors the displacement, decoupling it from the measurement update.
Empirical Validation: Instantiation of RPU within the DPS framework and evaluation on FFHQ and ImageNet datasets using both automatic metrics and human faithfulness studies.

4. Experimental Results

The authors evaluated RPU on FFHQ (256x256) and ImageNet (256x256) across three inverse problems: box inpainting, Gaussian deblurring, and motion deblurring.

Quantitative Metrics (FFHQ):
- Box Inpainting: RPU improved PSNR (19.72 $\to$ 20.40) and LPIPS (0.400 $\to$ 0.394). FID increased slightly (45.44 $\to$ 50.35), suggesting a trade-off where RPU sacrifices some distributional sharpness for instance faithfulness.
- Deblurring: RPU showed consistent improvements in PSNR and LPIPS for both Gaussian and motion deblurring tasks.
Human Faithfulness Studies:
- Blind Pairwise: In box inpainting, RPU received 91.9% of non-tie majority preferences over DPS.
- Ground-Truth-Assisted: When readers compared outputs against the ground truth, RPU received 91.1% of non-tie preferences in box inpainting.
- Deblurring: While blind comparisons resulted in many ties (indicating similar visual realism), ground-truth-assisted studies showed a strong preference for RPU (86.2% for Gaussian, 82.1% for motion deblurring), confirming that RPU reduces subtle, measurement-inconsistent details that are hard to detect blindly.
ImageNet Transfer: On ImageNet Gaussian deblurring, RPU improved PSNR (20.406 $\to$ 20.509). Human studies showed a preference for RPU in non-tie cases (72.7%), though the study was tie-heavy.

5. Significance and Claims

The paper claims that robustifying the prior update is a targeted and effective strategy for improving instance faithfulness in diffusion inverse solvers.

Mechanism: The results support the view that hallucinations often arise from the prior-side proposal before measurement correction. By stabilizing this specific step, RPU reduces the introduction of unsupported details.
Scope: The authors emphasize that RPU is not a universal replacement for reconstruction metrics or human inspection, nor is it a standalone hallucination detector. Its effectiveness is most pronounced in scenarios where the prior shapes weakly constrained content (e.g., large inpainting masks).
Limitations: The authors note that the method is task-dependent; in highly constrained tasks (like some deblurring scenarios) or broader distributions (ImageNet), the benefits are less dramatic and result in more "tie" outcomes in human studies. The claims are modest, positioning RPU as a specific intervention for improving faithfulness rather than a general solver improvement.