A Minimum Variance Path Principle for Accurate and Stable Score-Based Density Ratio Estimation
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Abstract (arXiv)
Score-based methods are powerful across machine learning, but they face a paradox: theoretically path-independent, yet practically path-dependent. We resolve this by proving that practical training objectives differ from the ideal, ground-truth objective by a crucial, overlooked term: the path variance of the score function. We propose the MVP (**M**imum **V**ariance **P**ath) Principle to minimize this path variance. Our key contribution is deriving a closed-form expression for the variance, making optimization tractable. By parameterizing the path with a flexible Kumaraswamy Mixture Model, our method learns data-adaptive, low-variance paths without heuristic manual selection. This principled optimization of the complete objective yields more accurate and stable estimators, establishing new state-of-the-art results on challenging benchmarks and providing a general framework for optimizing score-based interpolation. Our code can be found in https://github.com/Hoemr/OpenDRE.git.
Key facts. Cited by 3 papers in the map (data through 13 Oct 2026). Builds on 49 of its 76 references that are in the map. First posted on arXiv 31 Jan 2026.
Builds on
49 of 76 references.
References · 49
- 2020Denoising Diffusion Probabilistic Modelscited by 20,952
- 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,028
- 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,751
- 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,607
- 2017Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semanticscited by 1,348
- 2021Variational Diffusion Modelscited by 1,148
- 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 917
- 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 671
- 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 588
- 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 382
- 2024Guiding a Diffusion Model with a Bad Version of Itselfcited by 290
- 2019Diagnosing and Enhancing VAE Modelscited by 193
37 more
- 2020Telescoping Density-Ratio Estimationcited by 108
- 2024Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processescited by 64
- 2021Density Ratio Estimation via Infinitesimal Classificationcited by 61
- 2023Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimizationcited by 57
- 2023Diffusion Models With Learned Adaptive Noisecited by 51
- 2020Non-Negative Bregman Divergence Minimization for Deep Direct Density Ratio Estimationcited by 43
- 2023On Kinetic Optimal Probability Paths for Generative Modelscited by 42
- 2023Beyond Normal: On the Evaluation of Mutual Information Estimatorscited by 37
- 2025Variational Rectified Flow Matchingcited by 34
- 2021Featurized Density Ratio Estimationcited by 33
- 2024An analysis of the noise schedule for score-based generative modelscited by 25
- 2023Neural Diffusion Modelscited by 21
- 2024Sparse Inducing Points in Deep Gaussian Processes: Enhancing Modeling with Denoising Diffusion Variational Inferencecited by 16
- 2017Trimmed Density Ratio Estimationcited by 15
- 2023Provable benefits of annealing for estimating normalizing constants: Importance Sampling, Noise-Contrastive Estimation, and beyondcited by 13
- 2025Density Ratio Estimation with Conditional Probability Pathscited by 13
- 2025Dequantified Diffusion-Schr"odinger Bridge for Density Ratio Estimationcited by 11
- 2023SciRE-Solver: Accelerating Diffusion Models Sampling by Score-integrand Solver with Recursive Differencecited by 10
- 2025EVODiff: Entropy-aware Variance Optimized Diffusion Inferencecited by 10
- 2022TO-FLOW: Efficient Continuous Normalizing Flows with Temporal Optimization adjoint with Moving Speedcited by 8
- 2023Sparse Variational Student-t Processescited by 8
- 2024Density Ratio Estimation via Sampling along Generalized Geodesics on Statistical Manifoldscited by 8
- 2023Bayesian Gaussian Process ODEs via Double Normalizing Flowscited by 7
- 2020Learning Calibrated Uncertainties for Domain Shift: A Distributionally Robust Learning Approachcited by 6
- 2024Analytical Uncertainty-Based Loss Weighting in Multi-Task Learningcited by 6
- 2025Direct Density Ratio Optimization: A Statistically Consistent Approach to Aligning Large Language Modelscited by 6
- 2025Enhancing Adversarial Robustness with Conformal Prediction: A Framework for Guaranteed Model Reliabilitycited by 6
- 2023Direct Amortized Likelihood Ratio Estimationcited by 5
- 2024Entropy-Informed Weighting Channel Normalizing Flow for Deep Generative Modelscited by 5
- 2025Projection Pursuit Density Ratio Estimationcited by 5
- 2024Fully Bayesian Differential Gaussian Processes through Stochastic Differential Equationscited by 4
- 2024Variational Learning of Gaussian Process Latent Variable Models through Stochastic Gradient Annealed Importance Samplingcited by 4
- 2022Tighter Bound Estimation for Efficient Biquadratic Optimization Over Unit Spherescited by 3
- 2024Stabilizing the Kumaraswamy Distributioncited by 3
- 2025Diffusion Secant Alignment for Score-Based Density Ratio Estimationcited by 3
- 2025Information Theoretic Learning for Diffusion Models with Warm Startcited by 3
- 2025Riesz Regression As Direct Density Ratio Estimationcited by 3
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Citing papers per year: 2026: 3.
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