Victor M. Yeom-Song

Bernardo Williams, Victor M. Yeom-Song, Marcelo Hartmann et al.

We propose a method for learning and sampling from probability distributions supported on the simplex. Our approach maps the open simplex to Euclidean space via smooth bijections, leveraging the Aitchison geometry to define the mappings, and supports modeling categorical data by a Dirichlet interpolation that dequantizes discrete observations into continuous ones. This enables density modeling in Euclidean space through the bijection while still allowing exact recovery of the original discrete distribution. Compared to previous methods that operate on the simplex using Riemannian geometry or custom noise processes, our approach works in Euclidean space while respecting the Aitchison geometry, and achieves competitive performance on both synthetic and real-world data sets.

Victor M. Yeom-Song, Severi Rissanen, Arno Solin et al.

Diffusion models struggle to produce samples that respect constraints, a common requirement in scientific applications. Recent approaches have introduced regularization terms in the loss or guidance methods during sampling to enforce such constraints, but they bias the generative model away from the true data distribution. This is a problem when the constraint is misspecified, which is a common issue in scientific applications where constraint formulation is challenging. We propose to integrate guidance-inspired adjustments to the denoiser, instead of the loss or sampling loop. This achieves a soft inductive bias towards constraint-compliant samples. We show that these softly constrained denoisers exploit constraint knowledge to improve compliance over standard denoisers, while maintaining enough flexibility to deviate from it in case of misspecification with observed data.