One of the primary challenges in Bayesian inference on the parameters of a diffusion model from discrete observations is the unavailability of an analytical expression for the transition density function between consecutive observation times, which is needed to derive the likelihood function. Extending previous studies that solve Fokker-Planck (FP) type partial differential equations with Normalizing Flows, we propose a new Normalizing Flow architecture to learn the transition density function of the diffusion process between two observation times.
arXiv:2603. 18907v2 Announce Type: replace Abstract: We propose a new Neural Galerkin Normalizing Flow framework to approximate the transition probability density function of a diffusion process by solving the corresponding Fokker-Planck equation with an atomic initial distribution, parametrically with respect to the location of the initial mass.
By Riccardo Saporiti, Fabio Nobile
arXiv:2502. 07580v4 Announce Type: replace Abstract: We present a novel view of diffusion-like generative modeling from the perspective of iterative Gaussian posterior inference.
By Marten Lienen, Marcel Kollovieh, Stephan G\"unnemann
arXiv:2606. 09434v2 Announce Type: replace Abstract: Solving Fokker-Planck equations (FPEs) for multiple initial conditions typically requires repeated computations, leading to substantial computational costs.
By Li Zeng, Xiaoliang Wan, Yaobin Wang, Fabio Nobile, Tao Zhou
arXiv:2606. 09434v1 Announce Type: new Abstract: The Fokker-Planck equation (FPE) plays a pivotal role in describing the time evolution of probability density functions (PDFs) for systems governed by stochastic dynamics.
By Li Zeng, Xiaoliang Wan, Yaobin Wang, Fabio Nobile, Tao Zhou
arXiv:2601. 21026v2 Announce Type: replace-cross Abstract: Sampling configurations at thermodynamic equilibrium is a central challenge in statistical physics.
By Louis Grenioux, Maxence Noble
arXiv:2603. 27996v2 Announce Type: replace Abstract: Diffusion models have emerged as a powerful framework for generative tasks in deep learning.
By Nihal Sanjay Singh, Mazdak Mohseni-Rajaee, Shaila Niazi, Kerem Y. Camsari
arXiv:2606. 26592v1 Announce Type: cross Abstract: We propose latent-space diffusion posterior sampling (L-DPS), an approximate Bayesian framework for high-dimensional inverse problems governed by partial differential equations (PDEs).
By Yuanzhe Wang, Alexandre M. Tartakovsky
arXiv:2504. 01894v2 Announce Type: replace Abstract: We present a bifidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution.
By Caroline Tatsuoka, Minglei Yang, Dongbin Xiu, Guannan Zhang
arXiv:2605. 00161v2 Announce Type: replace Abstract: Diffusion language models (DLMs) are an attractive alternative to autoregressive models because they promise sublinear-time, parallel generation, yet practical gains remain elusive as high-quality samples still demand hundreds of refinement steps.
By Hasan Amin, Yuan Gao, Yaser Souri, Subhojit Som, Ming Yin, Rajiv Khanna, Xia Song
Stochastic-process models are, as a rule, far easier to simulate than to condition. Non-linear observations, non-Gaussian likelihoods, black-box information, and global constraints all induce intractable conditional laws, requiring bespoke, model-specific constructions.
arXiv:2512. 19196v4 Announce Type: replace-cross Abstract: Solving high-dimensional Fokker-Planck (FP) equations remains a challenging problem in computational physics and stochastic dynamics, due to the curse of dimensionality, unbounded domains, and complex probability landscapes.
By Xiaolong Wu, Qifeng Liao