Year: 2025
Type: preprint
Abstract: Estimating density ratios has become increasingly important with the recent rise of score-based and diffusion-inspired methods. However, current tangent-based approaches rely on a high-variance learning objective, which leads to unstable training and costly numerical integration during inference. We propose \textit{Interval-annealed Secant Alignment Density Ratio Estimation (ISA-DRE)}, a score-based framework along diffusion interpolants that replaces the instantaneous tangent with its interval integral, the secant, as the learning target. We show theoretically that the secant is a provably lower variance and smoother target for neural approximation, and also a strictly more general representation that contains the tangent as the infinitesimal limit. To make secant learning feasible, we introduce the \textit{Secant Alignment Identity (SAI)} to enforce self consistency between secant and tangent representations, and \textit{Contraction Interval Annealing (CIA)} to ensure stable convergence. Empirically, this stability-first formulation produces high efficiency and accuracy. ISA-DRE achieves comparable or superior results with fewer function evaluations, demonstrating robustness under large distribution discrepancies and effectively mitigating the density-chasm problem.
Source: arXiv (Cornell University)
Institutions: South China University of Technology, Columbia University, RIKEN
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414760941