Continuous-Time Flows for Efficient Inference and Density Estimation

TL;DR

This paper introduces continuous-time flows (CTFs), a diffusion-based framework that unifies efficient inference and density estimation with theoretical guarantees, outperforming existing methods like normalizing flows and GANs.

Contribution

The paper proposes continuous-time flows (CTFs), a novel diffusion-based approach that simultaneously addresses inference and density estimation within a single, theoretically grounded framework.

Findings

CTFs achieve competitive results on various tasks.

The framework provides theoretical guarantees for convergence.

Experiments show promising performance compared to related techniques.

Abstract

Two fundamental problems in unsupervised learning are efficient inference for latent-variable models and robust density estimation based on large amounts of unlabeled data. Algorithms for the two tasks, such as normalizing flows and generative adversarial networks (GANs), are often developed independently. In this paper, we propose the concept of {\em continuous-time flows} (CTFs), a family of diffusion-based methods that are able to asymptotically approach a target distribution. Distinct from normalizing flows and GANs, CTFs can be adopted to achieve the above two goals in one framework, with theoretical guarantees. Our framework includes distilling knowledge from a CTF for efficient inference, and learning an explicit energy-based distribution with CTFs for density estimation. Both tasks rely on a new technique for distribution matching within amortized learning. Experiments on various tasks demonstrate promising performance of the proposed CTF framework, compared to related techniques.