# Towards Healing the Blindness of Score Matching

arXiv: https://arxiv.org/abs/2209.07396 · HTML: https://mlsanity.com/paper/2209.07396/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 24 references that are in the map.
- First posted on arXiv 15 Sep 2022.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [A Kernel Test of Goodness of Fit](https://mlsanity.com/paper/1602.02964/) (2016)
- [Adversarial score matching and improved sampling for image generation](https://mlsanity.com/paper/2009.05475/) (2020)
- [Minimum Stein Discrepancy Estimators](https://mlsanity.com/paper/1906.08283/) (2019)
- [Learning deep kernels for exponential family densities](https://mlsanity.com/paper/1811.08357/) (2018)
- [Blindness of score-based methods to isolated components and mixing proportions](https://mlsanity.com/paper/2008.10087/) (2020)
- [Annealed Stein Variational Gradient Descent](https://mlsanity.com/paper/2101.09815/) (2021)
- [Measuring Sample Quality with Diffusions](https://mlsanity.com/paper/1611.06972/) (2016)
- [Spread Divergence](https://mlsanity.com/paper/1811.08968/) (2018)
- [Generalised Bayesian Inference for Discrete Intractable Likelihood](https://mlsanity.com/paper/2206.08420/) (2022)
- [Interpreting diffusion score matching using normalizing flow](https://mlsanity.com/paper/2107.10072/) (2021)

## Built on by (most cited first, 13 of 13)

- [Diffusive Gibbs Sampling](https://mlsanity.com/paper/2402.03008/) (2024)
- [Learning normalized image densities via dual score matching](https://mlsanity.com/paper/2506.05310/) (2025)
- [RNE: plug-and-play diffusion inference-time control and energy-based training](https://mlsanity.com/paper/2506.05668/) (2025)
- [Robust and Scalable Bayesian Online Changepoint Detection](https://mlsanity.com/paper/2302.04759/) (2023)
- [FEAT: Free energy Estimators with Adaptive Transport](https://mlsanity.com/paper/2504.11516/) (2025)
- [Energy Discrepancies: A Score-Independent Loss for Energy-Based Models](https://mlsanity.com/paper/2307.06431/) (2023)
- [Moment Matching Denoising Gibbs Sampling](https://mlsanity.com/paper/2305.11650/) (2023)
- [On the Robustness of Kernel Goodness-of-Fit Tests](https://mlsanity.com/paper/2408.05854/) (2024)
- [Training Energy-Based Normalizing Flow with Score-Matching Objectives](https://mlsanity.com/paper/2305.15267/) (2023)
- [Maximum Likelihood Learning of Unnormalized Models for Simulation-Based Inference](https://mlsanity.com/paper/2210.14756/) (2022)
- [A Unified View of Optimal Kernel Hypothesis Testing](https://mlsanity.com/paper/2503.07084/) (2025)
- [Using Perturbation to Improve Goodness-of-Fit Tests based on Kernelized Stein Discrepancy](https://mlsanity.com/paper/2304.14762/) (2023)
- [Fast and Scalable Score-Based Kernel Calibration Tests](https://mlsanity.com/paper/2510.14711/) (2025)

## Abstract (arXiv)

Score-based divergences have been widely used in machine learning and statistics applications. Despite their empirical success, a blindness problem has been observed when using these for multi-modal distributions. In this work, we discuss the blindness problem and propose a new family of divergences that can mitigate the blindness problem. We illustrate our proposed divergence in the context of density estimation and report improved performance compared to traditional approaches.