Reproduce “Score-Based Generative Modeling through Anisotropic Stochastic Partial Differential Equations” on OpenResearch

About this paper

Sascha Holl, Jente Vandersanden, Gurprit Singh, Hans-Peter Seidel

The authors introduce a geometry-aware stochastic partial differential equation for score-based image generation, making smoothing respond to gradients in the current image while noise corrupts it. A learned score guides the reverse process. On CIFAR-10, their anisotropic model reaches FID 2.0 versus 19.6 for their isotropic variant; this supports the approach in one implementation, not a general rule.

Key insights

• A geometry-aware forward process, where information degradation respects local image structures, provides richer structural cues to the score network, enabling more accurate score function learning.
• Dynamically adapting anisotropic diffusion coefficients allow for selective smoothing of homogeneous regions while preserving critical features like edges, which are essential for high-fidelity image reconstruction.
• Despite increased theoretical complexity, the proposed numerical scheme and design choices lead to a computationally efficient implementation, demonstrating lower training and inference costs compared to isotropic SDE-driven baselines.

Summary by alphaXiv.