The information geometry of product-reference discrete diffusion: Interaction growth complexity and optimal scheduling
We study a class of product-reference diffusion algorithms for sampling from a discrete distribution. We show that their sampling performance can be characterized using a path-based measure of data geometry that we call the interaction growth complexity (IGC). We show that a bivariate IGC kernel gives an exact representation of both the KL discretization error and a simple one-step upper bound. The simpler univariate IGC density can be used to study the effect of stepsize choices on the iteration complexity required to obtain $ε$-accurate samples in KL divergence. Samplers that traverse the path with equi-spaced steps in log-squared-reliability-odds have performance that depends on the ag...
| Authors | Martin J. Wainwright |
|---|---|
| Primary category | stat.ML |
| Published | 28 August 2026 |
| Last updated at source | 28 August 2026 |
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