Bernardo P. Schaeffer

arXiv2026

The Effect of Stochasticity in Score-Based Diffusion Sampling: a KL Divergence Analysis

Sampling in score-based diffusion models can be performed by solving either a reverse-time stochastic differential equation (SDE) parameterized by an arbitrary stochasticity function or a probability flow ODE, corresponding to setting this stochasticity function to zero. In this work, we investigate the effect of this stochasticity on the generation process through the evolution of Kullback-Leibler (KL) divergences, obtaining general KL divergence bounds and a novel analysis of the impact of the time-profile of the score error on model performance. For exact score functions, stochasticity has a contractive effect, decreasing KL divergence along the sampling trajectory. For approximate scores, however, a trade-off arises between correcting accumulated errors and amplifying current score errors, meaning stochasticity can either improve or degrade generation performance. Theoretical considerations indicate that the gain from stochasticity depends on the time-localization of the trained model error. We test this in experiments on both toy and benchmark data sets, also comparing the KL divergence evolution with the obtained bounds. We also present a fully analytical example, where all the relevant quantities can be computed, and the optimal stochasticity function can be characterized via an optimal control analysis.

cs.LG↗

arXiv2025

Controlled Latent Diffusion Models for 3D Porous Media Reconstruction

Note: The final version of this article was published in Computers and Geosciences, Volume 206, January 2026, 106038. DOI: 10.1016/j.cageo.2025.106038. Readers should refer to the published version for the most up-to-date content. Three-dimensional digital reconstruction of porous media presents a fundamental challenge in geoscience, requiring simultaneous resolution of fine-scale pore structures while capturing representative elementary volumes. We introduce a computational framework that addresses this challenge through latent diffusion models operating within the EDM framework. Our approach reduces dimensionality via a custom variational autoencoder trained in binary geological volumes, improving efficiency and also enabling the generation of larger volumes than previously possible with diffusion models. A key innovation is our controlled unconditional sampling methodology, which enhances distribution coverage by first sampling target statistics from their empirical distributions, then generating samples conditioned on these values. Extensive testing on four distinct rock types demonstrates that conditioning on porosity - a readily computable statistic - is sufficient to ensure a consistent representation of multiple complex properties, including permeability, two-point correlation functions, and pore size distributions. The framework achieves better generation quality than pixel-space diffusion while enabling significantly larger volume reconstruction (256-cube voxels) with substantially reduced computational requirements, establishing a new state-of-the-art for digital rock physics applications.

physics.geo-ph↗