# SD-KDE: Score-Debiased Kernel Density Estimation

arXiv: https://arxiv.org/abs/2504.19084 · HTML: https://mlsanity.com/paper/2504.19084/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 25 references that are in the map.
- First posted on arXiv 27 Apr 2025.

## Builds on (most cited first, 9 of 9)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [A Tutorial on Kernel Density Estimation and Recent Advances](https://mlsanity.com/paper/1704.03924/) (2017)
- [Sylvester Normalizing Flows for Variational Inference](https://mlsanity.com/paper/1803.05649/) (2018)
- [Kernel Density Estimation for Dynamical Systems](https://mlsanity.com/paper/1607.03792/) (2016)
- [Roundtrip: A Deep Generative Neural Density Estimator](https://mlsanity.com/paper/2004.09017/) (2020)

## Built on by (most cited first, 2 of 2)

- [Flash-SD-KDE: Accelerating SD-KDE with Tensor Cores](https://mlsanity.com/paper/2602.10378/) (2026)
- [Constant-Target Energy Matching: A Unified Framework for Continuous and Discrete Density Estimation](https://mlsanity.com/paper/2605.09085/) (2026)

## Abstract (arXiv)

We propose a novel method for density estimation that leverages an estimated score function to debias kernel density estimation (SD-KDE). In our approach, each data point is adjusted by taking a single step along the score function with a specific choice of step size, followed by standard KDE with a modified bandwidth. The step size and modified bandwidth are chosen to remove the leading order bias in the KDE. Our experiments on synthetic tasks in 1D, 2D and on MNIST, demonstrate that our proposed SD-KDE method significantly reduces the mean integrated squared error compared to the standard Silverman KDE, even with noisy estimates in the score function. These results underscore the potential of integrating score-based corrections into nonparametric density estimation.