Semi-Discrete Normalizing Flows through Differentiable Tessellation. (arXiv:2203.06832v3 [cs.LG] UPDATED)

Mapping between discrete and continuous distributions is a difficult task and
many have had to resort to heuristical approaches. We propose a
tessellation-based approach that directly learns quantization boundaries in a
continuous space, complete with exact likelihood evaluations. This is done
through constructing normalizing flows on convex polytopes parameterized using
a simple homeomorphism with an efficient log determinant Jacobian. We explore
this approach in two application settings, mapping from discrete to continuous
and vice versa. Firstly, a Voronoi dequantization allows …

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