Develop a theory of boundary fuzziness in locally snapping diffusion models

Develop an analytical theory of the fuzziness at the boundaries between regions that snap to different training patches in locally structured diffusion models, including a treatment of how region boundaries are carried across local patches.

Background

The paper distinguishes numerical fuzziness caused by finite-step integration from fuzziness near the edges of regions taking values associated with different training patches. The latter is analytically difficult because it requires tracking a notion of region boundary across multiple local patches. The authors leave the development of such a theory unresolved for future work.

References

There is a different notion of ’fuzziness’, which concerns the definition around the edges of regions of ±1. This is more difficult to treat analytically, requiring as it does a notion of ’region boundary’ carried across various local patches. We leave the interesting possibility of such a theory to future work.

— Information Spreading in Diffusion Models from Effective Field Theory  (2608.14308 - Neogi et al., 14 Aug 2026) in Section 3.4, Noise Scheduling and Noise in Spatial Correlations