Should the Boundary Term Be Learned in Reflected Diffusion? Conormal Trace and Reflection Masking
We study score learning for reflected diffusion on bounded domains. Reflection keeps trajectories feasible but does not ensure that the learned score satisfies the boundary behavior implied by the forward process. With implicit score matching, integration by parts leaves a boundary term, and we show that it depends on one scalar at each boundary point: the diffusion- weighted normal component of the score, or conormal trace. The no-flux condition fixes this value while leaving the re- maining boundary components unrestricted; under anisotropic diffusion it generally differs from the ordinary normal score component. On hyperrectangles, our parametrization enforces the required trace withou...
| Authors | Ziyue Wang, Takafumi Kanamori |
|---|---|
| Primary category | stat.ML |
| Published | 4 August 2026 |
| Last updated at source | 4 August 2026 |
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