REVIEW 9 cited by
Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach
read the original abstract
Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior sampling methods proposed for solving common BIPs rely on heuristic approximations to the generative process. To exploit the generative capability of DMs and avoid the usage of such approximations, we propose an ensemble-based algorithm that performs posterior sampling without the use of heuristic approximations. Our algorithm is motivated by existing works that combine DM-based methods with the sequential Monte Carlo (SMC) method. By examining how the prior evolves through the diffusion process encoded by the pre-trained score function, we derive a modified partial differential equation (PDE) governing the evolution of the corresponding posterior distribution. This PDE includes a modified diffusion term and a reweighting term, which can be simulated via stochastic weighted particle methods. Theoretically, we prove that the error between the true posterior distribution can be bounded in terms of the training error of the pre-trained score function and the number of particles in the ensemble. Empirically, we validate our algorithm on several inverse problems in imaging to show that our method gives more accurate reconstructions compared to existing DM-based methods.
Forward citations
Cited by 9 Pith papers
-
SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogate
URGE performs unbiased path-wise importance reweighting via Girsanov estimation for derivative-free inference-time scaling in diffusion models, proving equivalence to particle-wise SMC and outperforming baselines empirically.
-
SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogate
SURGE is an unbiased particle filter that fuses diffusion-model simulations with noisy observations via sequential Monte Carlo reweighting over diffusion trajectories.
-
Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential Monte Carlo on Path Measures
URGE performs unbiased inference-time scaling for diffusion models by attaching multiplicative path weights from Girsanov estimation and resampling trajectories, with a proven equivalence to prior particle-wise SMC schemes.
-
How Does the Lagrangian Guide Safe Reinforcement Learning through Diffusion Models?
ALGD augments the Lagrangian to locally convexify the energy landscape in diffusion models, stabilizing safe RL training and generation without changing optimal policies.
-
Provable Diffusion Posterior Sampling for Bayesian Inversion
A diffusion posterior sampler using Monte Carlo Langevin score estimation and warm start is proven to converge in Wasserstein-2 distance under semi-log-concavity and sub-Gaussian assumptions, and outperforms DPS/TV on...
-
An Unconditional Representation of the Conditional Score in Infinite-Dimensional Linear Inverse Problems
Derives the conditional score exactly from an unconditional score via affine maps for linear inverse problems in infinite dimensions, shifting computation to offline training.
-
Provable diffusion-based posterior sampling for linear inverse problems via DDIM
A SVD-based, coordinate-wise DDIM sampler is claimed to asymptotically sample from the posterior for noisy linear inverse problems, but the proof's posterior identification step does not follow from the stated updates.
-
Consistency Regularised Gradient Flows for Inverse Problems
A consistency-regularized Euclidean-Wasserstein-2 gradient flow performs joint posterior sampling and prompt optimization in latent space for efficient low-NFE inverse problem solving with diffusion models.
-
Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects
A survey organizing AI methods for inverse PDE problems into inverse problems, inverse design, and control categories, covering applications and future challenges like physics-informed models and uncertainty quantification.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.