Dequantified Diffusion Schr""odinger Bridge for Density Ratio Estimation

2025-05-08

AI Summary

Existing density ratio estimation methods suffer from density and support gaps when source and target distributions differ significantly and exhibit insufficient support overlap; moreover, unbounded time scores near distribution boundaries cause training instability. This paper proposes D³RE, a unified framework introducing the first dequantized diffusion bridge interpolator (DDBI) and dequantized Schrödinger bridge interpolator (DSBI). By integrating diffusion processes, Gaussian dequantization, optimal transport, and Schrödinger bridge theory, D³RE establishes a two-stage interpolation mechanism that simultaneously expands support coverage and ensures bounded time scores. We provide theoretical guarantees of uniform approximation and stability. Empirically, D³RE achieves substantial improvements over baselines in mutual information estimation and density estimation tasks—exhibiting controlled convergence of time scores, enhanced accuracy, and superior robustness.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Density ratio estimation is fundamental to tasks involving $f$-divergences, yet existing methods often fail under significantly different distributions or inadequately overlap supports, suffering from the extit{density-chasm} and the extit{support-chasm} problems. Additionally, prior approaches yield divergent time scores near boundaries, leading to instability. We propose $ ext{D}^3 ext{RE}$, a unified framework for robust and efficient density ratio estimation. It introduces the Dequantified Diffusion-Bridge Interpolant (DDBI), which expands support coverage and stabilizes time scores via diffusion bridges and Gaussian dequantization. Building on DDBI, the Dequantified Schr""odinger-Bridge Interpolant (DSBI) incorporates optimal transport to solve the Schr""odinger bridge problem, enhancing accuracy and efficiency. Our method offers uniform approximation and bounded time scores in theory, and outperforms baselines empirically in mutual information and density estimation tasks.

Problem

• Addresses density-chasm and support-chasm in ratio estimation
• Stabilizes divergent time scores near distribution boundaries
• Improves accuracy via optimal transport in Schrödinger bridge

Innovation

• Dequantified Diffusion-Bridge Interpolant expands support coverage
• Dequantified Schrödinger-Bridge Interpolant enhances accuracy via optimal transport
• Unified framework ensures robust density ratio estimation