# Dequantified Diffusion-Schr"odinger Bridge for Density Ratio Estimation

arXiv: https://arxiv.org/abs/2505.05034 · HTML: https://mlsanity.com/paper/2505.05034/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 43 references that are in the map.
- First posted on arXiv 8 May 2025.

## Builds on (most cited first, 24 of 24)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2309.16948/) (2023)
- [Telescoping Density-Ratio Estimation](https://mlsanity.com/paper/2006.12204/) (2020)
- [Likelihood-free inference by ratio estimation](https://mlsanity.com/paper/1611.10242/) (2016)
- [Density Ratio Estimation via Infinitesimal Classification](https://mlsanity.com/paper/2111.11010/) (2021)
- [Non-Negative Bregman Divergence Minimization for Deep Direct Density Ratio Estimation](https://mlsanity.com/paper/2006.06979/) (2020)
- [A Novel Estimator of Mutual Information for Learning to Disentangle Textual Representations](https://mlsanity.com/paper/2105.02685/) (2021)
- [Featurized Density Ratio Estimation](https://mlsanity.com/paper/2107.02212/) (2021)
- [Accurate and Conservative Estimates of MRF Log-likelihood using Reverse Annealing](https://mlsanity.com/paper/1412.8566/) (2014)
- [Estimating the Density Ratio between Distributions with High Discrepancy using Multinomial Logistic Regression](https://mlsanity.com/paper/2305.00869/) (2023)
- [Sparse Inducing Points in Deep Gaussian Processes: Enhancing Modeling with Denoising Diffusion Variational Inference](https://mlsanity.com/paper/2407.17033/) (2024)
- [SciRE-Solver: Accelerating Diffusion Models Sampling by Score-integrand Solver with Recursive Difference](https://mlsanity.com/paper/2308.07896/) (2023)
- [Game-Theoretic Defenses for Robust Conformal Prediction Against Adversarial Attacks in Medical Imaging](https://mlsanity.com/paper/2411.04376/) (2024)
- [Density Ratio Estimation via Sampling along Generalized Geodesics on Statistical Manifolds](https://mlsanity.com/paper/2406.18806/) (2024)
- [Enhancing In-Context Learning via Implicit Demonstration Augmentation](https://mlsanity.com/paper/2407.00100/) (2024)

## Built on by (most cited first, 11 of 11)

- [EVODiff: Entropy-aware Variance Optimized Diffusion Inference](https://mlsanity.com/paper/2509.26096/) (2025)
- [Diffusion Bridge Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/2509.19078/) (2025)
- [Diffusion Secant Alignment for Score-Based Density Ratio Estimation](https://mlsanity.com/paper/2509.04852/) (2025)
- [A Minimum Variance Path Principle for Accurate and Stable Score-Based Density Ratio Estimation](https://mlsanity.com/paper/2602.00834/) (2026)
- [Towards Disentangled Preference Optimization Dynamics: Suppress the Loser, Preserve the Winner](https://mlsanity.com/paper/2604.18239/) (2026)
- [Learning Energy-Based Models from Stochastic Interpolants using Spatiotemporal Differences](https://mlsanity.com/paper/2605.26850/) (2026)
- [One-Step Score-Based Density Ratio Estimation](https://mlsanity.com/paper/2604.10672/) (2026)
- [Local-Time Riemannian Score Matching on the Quantum Pure-State Manifold](https://mlsanity.com/paper/2605.03573/) (2026)
- [DiFA: Inference-Time Forward-Process Alignment for Diffusion Models](https://mlsanity.com/paper/2607.17972/) (2026)
- [Instance Relation Learning Network with Label Knowledge Propagation for Few-shot Multi-label Intent Detection](https://mlsanity.com/paper/2510.07776/) (2025)
- [Implicit Variational Rejection Sampling](https://mlsanity.com/paper/2606.14235/) (2026)

## Abstract (arXiv)

Density ratio estimation is fundamental to tasks involving f-divergences, yet existing methods often fail under significantly different distributions or inadequately overlapping supports -- the density-chasm and the support-chasm problems. Additionally, prior approaches yield divergent time scores near boundaries, leading to instability. We design D3RE, a unified framework for robust, stable and efficient density ratio estimation. We propose the dequantified diffusion bridge interpolant (DDBI), which expands support coverage and stabilizes time scores via diffusion bridges and Gaussian dequantization. Building on DDBI, the proposed 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.