Lattice Random Walk Discretisations of Stochastic Differential Equations

2025/08/28 by Samuel Duffield, Maxwell Aifer, Duffield, Samuel +7 · 1 voice
#math.NA #cs.ET #stat.CO

paper · pdf · doi:10.48550/arxiv.2508.20883

Abstract

We introduce a lattice random walk discretisation scheme for stochastic differential equations (SDEs) that samples binary or ternary increments at each step, suppressing complex drift and diffusion computations to simple 1 or 2 bit random values. This approach is a significant departure from traditional floating point discretisations and offers several advantages; including compatibility with stochastic computing architectures that avoid floating-point arithmetic in place of directly manipulating the underlying probability distribution of a bitstream, elimination of Gaussian sampling requirements, robustness to quantisation errors, and handling of non-Lipschitz drifts. We prove weak convergence and demonstrate the advantages through experiments on various SDEs, including state-of-the-art diffusion models.

Citations

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Discussions

• Read more at arxiv.org/abs/2508.20883 Including scaling LRW up to image generation with Stable Diffusion 3.5 🐱 [bsky, 5 points, 0 comments]

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