{"ID":2874132,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.04852","arxiv_id":"2509.04852","title":"Diffusion Secant Alignment for Score-Based Density Ratio Estimation","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.","short_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{Int...","url_abs":"https://arxiv.org/abs/2509.04852","url_pdf":"https://arxiv.org/pdf/2509.04852v3","authors":"[\"Wei Chen\",\"Shigui Li\",\"Jiacheng Li\",\"Jian Xu\",\"Zhiqi Lin\",\"Junmei Yang\",\"Delu Zeng\",\"John Paisley\",\"Qibin Zhao\"]","published":"2025-09-05T07:06:56Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\"]","methods":"[\"Diffusion Model\"]","has_code":false}