arXiv:2604. 16461v2 Announce Type: replace-cross Abstract: Physics-guided sampling with diffusion priors has recently shown strong performance in solving complex systems of partial differential equations (PDEs) from sparse observations.
arXiv:2604. 17838v2 Announce Type: replace Abstract: Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.
arXiv:2602. 09708v2 Announce Type: replace-cross Abstract: We propose physics-informed spectral diffusion (PISD), a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of partial differential equations (PDEs) conditioned on partial observations, which includes, in particular, forward and inverse PDE problems.
The paper introduces Self-Augmented Diffusion Guidance, a physics-informed method that augments diffusion models with self-generated data to enforce physical law constraints. By conditioning the data distribution on the deviation from correct dynamics and setting this deviation to zero during generation, the approach decouples equation evaluation from training and sampling, avoiding costly numerical solves. Experiments show the method markedly reduces deviations versus standard diffusion models and further improves results when combined with existing physics-constrained diffusion techniques.
The paper introduces a physics‑informed diffusion guidance technique that uses self‑generated data augmentation to condition the diffusion model on the deviation from physical laws. By setting this deviation to zero during sampling, the method decouples equation evaluation from training and sampling, eliminating the need to solve governing equations at each denoising step. Experiments show the approach substantially reduces deviations from true dynamics and further improves performance when combined with existing physics‑constrained diffusion methods.
The paper investigates training diffusion models to sample from distributions defined by unnormalized densities or energy functions. It benchmarks various diffusion-structured inference techniques, including simulation-based variational methods and off-policy approaches such as continuous generative flow networks, highlighting their relative strengths and challenging some prior claims. Additionally, the authors introduce a new exploration strategy for off-policy methods that employs local search in the target space with a replay buffer, demonstrating improved sample quality across multiple target distributions.
arXiv:2511. 17038v4 Announce Type: replace Abstract: From a Bayesian perspective, score-based diffusion solves inverse problems through joint inference, embedding the likelihood with the prior to guide the sampling process.
arXiv:2506. 13058v2 Announce Type: replace-cross Abstract: Diffusion probabilistic models (DPMs) have demonstrated remarkable success in visual generation.
arXiv:2505. 22391v2 Announce Type: replace-cross Abstract: Modeling physical systems in a generative manner offers several advantages, including the ability to handle partial observations, generate diverse solutions, and address both forward and inverse problems.
arXiv:2601. 21284v2 Announce Type: replace-cross Abstract: Diffusion models have emerged as powerful generative tools for modeling complex data distributions, yet their purely data-driven nature limits applicability in engineering and scientific problems where physical laws must be respected.
arXiv:2602. 16634v2 Announce Type: replace-cross Abstract: The rare-event sampling problem has long been the central limiting factor in molecular dynamics (MD), especially in biomolecular simulation.
arXiv:2605. 00337v2 Announce Type: replace Abstract: Sampling the distribution of collective variables (CVs) and estimating the associated free energy surface are crucial problems in statistical physics, as they underpin a better understanding of chemical reactions and conformational transitions.
arXiv:2512. 08022v2 Announce Type: replace-cross Abstract: We propose a novel diffusion-based posterior sampling method within a plug-and-play framework.