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:2607. 14398v1 Announce Type: cross Abstract: Constrained generative models aim to produce samples that satisfy complex feasibility constraints while remaining faithful to the data distribution.
arXiv:2606. 15359v1 Announce Type: new Abstract: Diffusion models have emerged as powerful tools for planning and control by learning multimodal distributions over actions and trajectories.
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:2609.15702v1 Announce Type: new Abstract: Pretrained score-based diffusion models provide strong unconditional priors, yet enforcing measurement or physics consistency in inverse problems is of...
The paper introduces a new method for perturbing data distributions in a way that respects equality constraints, allowing generative models to better handle constrained data. By adjusting the distribution while preserving the manifold geometry, the approach ensures support matches the ambient space dimension. Experiments with diffusion models and normalizing flows demonstrate improved data recovery and stable sampling across several tasks.
arXiv:2607. 00095v1 Announce Type: cross Abstract: Generative models have emerged as scalable surrogates for physical simulation, yet they offer no guarantee that their outputs respect the conservation laws, boundary conditions, and nonlinear invariants that govern the underlying physics.
arXiv:2606. 16138v1 Announce Type: cross Abstract: Recovering dynamical systems from noisy observations is a recurring challenge across scientific domains, including neuroscience and physics.
arXiv:2602.12624v2 Announce Type: replace Abstract: Diffusion-based generative models have achieved remarkable performance across various domains, yet their practical deployment is often limited by h...
arXiv:2602. 21429v3 Announce Type: replace Abstract: Flow-based generative models, such as diffusion models and flow matching models, have achieved remarkable success in learning complex data distributions.
The paper introduces Hessian-free high-resolution (HFHR) dynamics, an extension of underdamped Langevin dynamics that incorporates reversible position diffusion for sampling in machine learning. It provides an explicit quantitative contraction rate under a position Poincaré inequality, weighted Hessian and Laplacian bounds, and a compact Sobolev embedding, even when the potential is non‑convex. For the HFHR Monte Carlo algorithm, a path‑space Girsanov argument yields a non‑asymptotic convergence bound and an explicit iteration complexity in total variation distance, improving on previous HFHR results and demonstrating benefits of a positive diffusion parameter through numerical experiments.
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:2609. 22752v1 Announce Type: new Abstract: Diffusion models have demonstrated strong power in generative modeling tasks across multiple domains, exhibiting a remarkable capability of learning complex distributions from samples.