NeurIPS 2025

Go With the Flow: Fast Diffusion for Gaussian
Mixture Models
George Rapakoulias 1 ∗
Ali Reza Pedram 1,2
Fengjiao Liu 3
Lingjiong Zhu 4
Panagiotis Tsiotras 1
1 Department of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA
2 School of Computer Science, University of Oklahoma, Norman, OK
3 Department of ECE, FAMU-FSU College of Engineering, Tallahassee, FL
4 Department of Mathematics, Florida State University, Tallahassee, FL
Abstract
Schr¨odinger Bridges (SBs) are diffusion processes that steer, in finite time, a given
initial distribution to another final one while minimizing a suitable cost functional.
Although various methods for computing SBs have recently been proposed in the
literature, most of these approaches require computationally expensive training
schemes, even for solving low-dimensional problems. In this work, we propose
an analytic parametrization of a set of feasible policies for steering the distribution
of a dynamical system from one Gaussian Mixture Model (GMM) to another. In-
stead of relying on standard non-convex optimization techniques, the optimal pol-
icy within the set can be approximated as the solution of a low-dimensional linear
program whose dimension scales linearly with the number of components in each
mixture. The proposed method generalizes naturally to more general classes of
dynamical systems, such as controllable linear time-varying systems, enabling ef-
ficient solutions to multi-marginal momentum SBs between GMMs, a challenging
distribution interpolation problem. We showcase the potential of this approach in
low-to-moderate dimensional problems such as image-to-image translation in the
latent space of an autoencoder, learning of cellular dynamics using multi-marginal
momentum SBs, and various other examples. The implementation is publicly
available at https://github.com/georgeRapa/GMMflow.
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Introduction and Background
The problem of finding mappings between distributions of data, originally known as the Optim...