Diffusion Priors

Physics-guided sampling with diffusion priors has recently shown strong performance in solving complex systems of partial differential equations (PDEs) from sparse observations. However, these methods are typically evaluated on benchmark problems that do not fully demonstrate their ability to generate temporally consistent solutions of time-dependent PDEs, often focusing instead on reconstructing a single snapshot. In this work, we apply these methods to gas-phase reaction kinetics problems governed by the advection-reaction-diffusion (ARD) equation, providing a setting that more closely reflects realistic laboratory experiments. We demonstrate that guided sampling can be used to reconstruct full spatiotemporal trajectories, rather than isolated states. Furthermore, we show that these methods generalise to previously unseen parameter regimes, highlighting their potential for real-world applications.

This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a diffusion process. In this context, the issue of posterior sampling is known to be thorny, and a recent paper proposes a notably simple and effective solution. Additionally, it opens an remarkable flexibility when it comes to estimating observation parameters. The proposed strategy enables to define an optimal estimator for both observation parameters and image of interest. Furthermore, the strategy provides a means for uncertainty quantification. In addition, MCMC algorithms allow for the computation of estimates and properties of posteriors, while offering some guarantees. The paper presents several numerical experiments that clearly confirm the computational efficiency and the quality of both estimates and uncertainty quantification.

Pre-trained Latent Diffusion Models (LDMs) have recently shown strong perceptual priors for low-level vision tasks, making them a promising direction for multi-exposure High Dynamic Range (HDR) reconstruction. However, directly applying LDMs to HDR remains challenging due to: (1) limited dynamic-range representation caused by 8-bit latent compression, (2) high inference cost from multi-step denoising, and (3) content hallucination inherent to their generative nature. To address these challenges, we introduce GMODiff, a gain map-driven one-step diffusion framework for multi-exposure HDR reconstruction. Instead of reconstructing full HDR content, we reformulate HDR reconstruction as a degradation-aware Gain Map (GM) refinement problem, where the GM encodes the extended dynamic range while retaining the same bit depth as LDR images. We initialize the denoising process from an informative regression-based estimate rather than pure noise, allowing the model to generate high-quality GMs in a single denoising step. Furthermore, recognizing that regression-based models excel in content fidelity while LDMs favor perceptual quality, we leverage regression priors to guide both the denoising process and latent decoding of the LDM, suppressing hallucinations while preserving structural accuracy. Extensive experiments demonstrate that GMODiff performs favorably against several state-of-the-art methods and is 100x faster than previous LDM-based methods. Code is available at https://github.com/gbymat/GMODiff.

From a Bayesian perspective, score-based diffusion solves inverse problems through joint inference, embedding the likelihood with the prior to guide the sampling process. However, this formulation fails to explain its practical behavior: the prior offers limited guidance, while reconstruction is largely driven by the measurement-consistency term, leading to an inference process that is effectively decoupled from the diffusion dynamics. We show that the diffusion prior in these solvers functions primarily as a warm initializer that places estimates near the data manifold, while reconstruction is driven almost entirely by measurement consistency. Based on this observation, we introduce \textbf{DAPS++}, which fully decouples diffusion-based initialization from likelihood-driven refinement, allowing the likelihood term to guide inference more directly while maintaining numerical stability and providing insight into why unified diffusion trajectories remain effective in practice. By requiring fewer function evaluations (NFEs) and measurement-optimization steps, \textbf{DAPS++} achieves high computational efficiency and robust reconstruction performance across diverse image restoration tasks.

This work introduces MedForj, a suite of 3D foundational generative priors based on diffusion models. The MedForj models were trained on $72{,}659$ 1~mm isotropic 3D $T_1$-weighted MRI human brain image volumes from $38{,}174$ subjects, drawn from a curated corpus of $80{,}675$ volumes from $42{,}506$ subjects spanning $38$ publicly available datasets. These training images were manually inspected to exclude those with poor quality and excessive pathology, and otherwise were minimally processed. The models include six different diffusion training strategies: rectified flow, latent diffusion rectified flow, flow matching, velocity prediction, clean prediction, and noise prediction. Image samples produced by each of these models were compared to each other and against real, ground truth data under downstream segmentation distributions, FID, five inverse problems, and blind human inspection in an observer study. Flow matching was the strongest strategy overall, achieving the best inverse problem solving results at $28.80$~dB PSNR and $0.874$ SSIM averaged over the five forward problems, the highest rate of reconstructions judged real by blind human raters at $72.6\%$, and the closest per-structure match to real segmented anatomy in a permutation test. It was not best everywhere: rectified flow produced the most convincing unconditional samples in the observer study and the best FID, and the latent rectified-flow model achieved the smallest joint distributional distance to real anatomy. No other strategy, however, performed consistently well across all four evaluations. We therefore recommend flow matching as the default MedForj prior, while releasing every strategy so that the choice can be revisited per application. All model weights and corresponding code are publicly available at https://github.com/piksl-research/medforj.

How can we reconstruct 3D hand poses when large portions of the hand are heavily occluded by itself or by objects? Humans often resolve such ambiguities by leveraging contextual knowledge -- such as affordances, where an object's shape and function suggest how the object is typically grasped. Inspired by this observation, we propose a generative prior for hand pose refinement guided by affordance-aware textual descriptions of hand-object interactions (HOI). Our method employs a diffusion-based generative model that learns the distribution of plausible hand poses conditioned on affordance descriptions, which are inferred from a large vision-language model (VLM). This enables the refinement of occluded regions into more accurate and functionally coherent hand poses. Extensive experiments on HOGraspNet, a 3D hand-affordance dataset with severe occlusions, demonstrate that our affordance-guided refinement significantly improves hand pose estimation over both recent regression methods and diffusion-based refinement lacking contextual reasoning.

We present StableMotion, a novel framework that leverages geometric and content priors from pretrained large-scale image diffusion models for motion estimation in single-image rectification tasks such as Stitched Image Rectangling (SIR) and Rolling Shutter Correction (RSC). Specifically, StableMotion takes a text-to-image Stable Diffusion (SD) model as its backbone and repurposes it as an image-to-motion estimator. To mitigate inconsistent outputs produced by diffusion models, we propose Adaptive Ensemble Strategy (AES), which consolidates multiple outputs into a cohesive, high-fidelity result. Additionally, we present Sampling Steps Disaster (SSD), a counterintuitive phenomenon in which increasing the number of sampling steps can lead to poorer outcomes, motivating our one-step inference design. StableMotion is evaluated on two image rectification tasks and delivers state-of-the-art performance on both, while also showing promising transferability through qualitative examples and no-reference evaluations on unseen SIR-OOD and real-captured RSC benchmarks. Supported by SSD, StableMotion achieves efficient one-step inference, offering over 100$\times$ speedup compared to previous diffusion model-based methods even when combined with the optional AES post-processing. Code and weights are available at https://github.com/ivowang/StableMotion.

Latent generative models have emerged as powerful priors for solving inverse problems. These models typically represent a class of natural signals at a single, fixed complexity, governed by the latent dimensionality. This can be limiting: depending on the problem, a latent dimensionality that is too small may result in high representation error, while one that is too large may overfit to noise. We develop tunable latent priors for diffusion models, normalizing flows, and variational autoencoders, leveraging nested dropout. Across tasks including compressed sensing, inpainting, denoising, and phase retrieval, we show empirically that tunable priors consistently achieve lower reconstruction errors than fixed-complexity baselines. In the linear denoising setting, we derive the optimal complexity in closed form, showing how it depends on the noise level and the signal spectrum. This work demonstrates the potential of tunable latent generative priors and motivates both the development of supporting theory and their application across a wide range of inverse problems.