A Hyperfinite Framework for Score-Based Generative Modeling
Score-based diffusion models are typically formulated using continuous-time stochastic differential equations and measure-theoretic stochastic calculus. In this paper, we develop a hyperfinite formulation of score-based generative modeling within the framework of Nonstandard Analysis. Starting from an internal diffusion process on a hyperfinite grid, we derive the associated infinitesimal generator and establish its correspondence with the classical Fokker--Planck equation. We then obtain a hyperfinite backward-mean identity that yields the reverse-time drift and provides a constructive derivation of the reverse-time SDE. Building on these results, we show that minimization of an internal...
| Authors | Sunder Ram Krishnan |
|---|---|
| Primary category | stat.ML |
| Published | 3 August 2026 |
| Last updated at source | 3 August 2026 |
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