Finite-Time Analysis of Discrete-Time Stochastic Interpolants
This work addresses the problem of efficient discrete-time stochastic interpolant analysis for researchers and practitioners in the field of generative models, providing an incremental yet significant step forward in the understanding of stochastic interpolant frameworks.
This work tackles the problem of discrete-time analysis of stochastic interpolants, achieving a finite-time upper bound on distribution estimation error, with results showing how factors like distance between distributions and estimation accuracy affect convergence rate. The bound quantifies the impact of these factors on convergence.
The stochastic interpolant framework offers a powerful approach for constructing generative models based on ordinary differential equations (ODEs) or stochastic differential equations (SDEs) to transform arbitrary data distributions. However, prior analyses of this framework have primarily focused on the continuous-time setting, assuming a perfect solution of the underlying equations. In this work, we present the first discrete-time analysis of the stochastic interpolant framework, where we introduce an innovative discrete-time sampler and derive a finite-time upper bound on its distribution estimation error. Our result provides a novel quantification of how different factors, including the distance between source and target distributions and estimation accuracy, affect the convergence rate and also offers a new principled way to design efficient schedules for convergence acceleration. Finally, numerical experiments are conducted on the discrete-time sampler to corroborate our theoretical findings.