Title: Score-based generative modeling through anisotropic SPDEs
Primary area: generative models
Keywords: generative modeling, score-based generative modeling, stochastic differential equations, stochastic partial differential equations, sde, spde, image generation, generative image modeling, score-based generative image modeling, numerical simulation, numerical spde

Abstract: Score-based generative modeling (SBGM) has achieved state-of-the-art performance in image generation, with the quality of generated images highly dependent on the design of the forward (diffusion) process. Among these, models based on stochastic differential equations have proven particularly effective.
 
While traditional methods aim to progressively destroy all image information to enable reconstruction from pure noise, we introduce a novel class of anisotropic stochastic partial differential equations (SPDEs) that preserve the geometric structure of the data throughout the transformation. These SPDEs consist of a drift term that enforces deterministic destruction via structured smoothing, and a diffusion coefficient that enables random destruction through noise injection. Both components are governed by anisotropy coefficients, enabling controlled, direction-dependent information degradation. 

This framework provides the theoretical foundation for a novel anisotropic SBGM. Due to geometry-aware degradation, the data generation process can exploit residual geometric cues, leading to improved fidelity in image reconstruction. We empirically validate this improvement in a proof-of-concept implementation on unconditional image generation, showing that anisotropic diffusion can achieve superior image quality metrics.

TL;DR: Score-based generative image modeling with geometric-aware transformations described by anisotropic stochastic partial differential equations