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:2607. 19173v1 Announce Type: new Abstract: Neural stochastic differential equations (SDEs) have emerged as powerful tools for learning noisy or stochastic dynamics directly from data; however, existing approaches largely assume uncoupled and continuous noise, limiting their applicability to realistic stochastic drivers, and often scale poorly in time, requiring expensive autoregressive training.
By Arthur Bizzi, Olga Fink
arXiv:2607. 12922v1 Announce Type: cross Abstract: Stochastic-process models are, as a rule, far easier to simulate than to condition.
By Louis Sharrock, Lachlan Astfalck, Henry Moss
arXiv:2602. 08733v2 Announce Type: replace Abstract: Ordinary differential equations (ODEs) are central to scientific modelling, but inferring their vector fields from noisy trajectories remains challenging.
By Maximilian Mauel, Johannes R. H\"ubers, David Berghaus, Patrick Seifner, Ramses J. Sanchez
The paper presents an amortized neural sampler that merges operator learning with flow-based methods to efficiently sample from invariant measures of stochastic differential equations (SDEs). By mapping SDE coefficient functions to pushforwards from a reference measure, the approach shifts the sampling cost to an initial training phase, after which new SDE instances can be sampled with a single encoder pass and a few ODE solver steps, independent of mixing time. The framework incorporates Lagrangian trajectory sensors and cross attention to handle high-dimensional problems, and the authors provide theoretical guarantees of expressivity and resolution invariance, demonstrating competitive accuracy and significant speedups over MCMC in 1D, 2D, and 64D SDE families.
By Lin Guo, Li Lei, Jingtong Zhang
The paper argues that the concrete random noise used in diffusion models is not merely a passive perturbation but a learnable input that can be exploited by the model. By analyzing how clean data and realized noise jointly form the noisy input, the authors show that the model can learn regularities in the data or in the noise structure, and that these two routes can interact. Experiments on MNIST and CIFAR‑10 using pseudorandom streams demonstrate that structured‑noise training can reduce prediction loss, but this advantage disappears when test noise is replaced with IID noise, indicating that the learned dependence is tied to the specific noise structure.
By Shengzhi Deng, Chenqi Ye, Yanze Guo