Sinkhorn-Drifting Generative Models

2026-03-12

AI Summary

This work addresses the instability, temperature sensitivity, and lack of convergence guarantees in existing drifting generative models at low temperatures. By establishing a theoretical equivalence between drifting dynamics and the gradient flow induced by Sinkhorn divergence, we propose a novel generative model featuring a cross-minus-self structure whose equilibrium state provably converges to the target distribution. Our approach reveals, for the first time, a fundamental connection between drifting dynamics and entropy-regularized optimal transport, thereby filling a critical gap in identifiability theory and enabling a continuous interpolation from one-sided normalization to two-sided Sinkhorn scaling. Experiments demonstrate substantial improvements: on FFHQ-ALAE, the FID at low temperature drops from 187.7 to 37.1 and the latent-space EMD decreases from 453.3 to 144.4; on MNIST, the model maintains full class coverage across all temperatures, significantly enhancing both generation quality and stability.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We establish a theoretical link between the recently proposed "drifting" generative dynamics and gradient flows induced by the Sinkhorn divergence. In a particle discretization, the drift field admits a cross-minus-self decomposition: an attractive term toward the target distribution and a repulsive/self-correction term toward the current model, both expressed via one-sided normalized Gibbs kernels. We show that Sinkhorn divergence yields an analogous cross-minus-self structure, but with each term defined by entropic optimal-transport couplings obtained through two-sided Sinkhorn scaling (i.e., enforcing both marginals). This provides a precise sense in which drifting acts as a surrogate for a Sinkhorn-divergence gradient flow, interpolating between one-sided normalization and full two-sided Sinkhorn scaling. Crucially, this connection resolves an identifiability gap in prior drifting formulations: leveraging the definiteness of the Sinkhorn divergence, we show that zero drift (equilibrium of the dynamics) implies that the model and target measures match. Experiments show that Sinkhorn drifting reduces sensitivity to kernel temperature and improves one-step generative quality, trading off additional training time for a more stable optimization, without altering the inference procedure used by drift methods. These theoretical gains translate to strong low-temperature improvements in practice: on FFHQ-ALAE at the lowest temperature setting we evaluate, Sinkhorn drifting reduces mean FID from 187.7 to 37.1 and mean latent EMD from 453.3 to 144.4, while on MNIST it preserves full class coverage across the temperature sweep. Project page: https://mint-vu.github.io/SinkhornDrifting/

Problem

• Sinkhorn divergence
• drifting generative models
• identifiability
• gradient flows
• entropic optimal transport

Innovation

• Sinkhorn divergence
• drifting generative models
• entropic optimal transport
• gradient flow
• cross-minus-self decomposition