Should the Boundary Term Be Learned in Reflected Diffusion? Conormal Trace and Reflection Masking

This paper studies score learning for reflected diffusion on bounded domains. It argues that implicit score matching leaves a boundary term determined by the score’s diffusion-weighted normal component, called the conormal trace. The no-flux condition fixes this scalar but not the remaining boundary components, especially under anisotropic diffusion. The authors propose parameterizations for hyperrectangles, simplices, and polygonal domains, and identify “reflection masking”: hard reflection can preserve feasibility while hiding an incorrect boundary trace. Reported experiments find clearer differences with infrequent reflection, anisotropic noise, and probability mass near constraint intersections.