mlsanityData to 7 Oct 2026

Sliced Score Matching: A Scalable Approach to Density and Score Estimation

arXiv 1905.07088 ↗First posted 17 May 2019cs.LG stat.MLcited by 381

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Cited by 195 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Score matching is a popular method for estimating unnormalized statistical models. However, it has been so far limited to simple, shallow models or low-dimensional data, due to the difficulty of computing the Hessian of log-density functions. We show this difficulty can be mitigated by projecting the scores onto random vectors before comparing them. This objective, called sliced score matching, only involves Hessian-vector products, which can be easily implemented using reverse-mode automatic differentiation. Therefore, sliced score matching is amenable to more complex models and higher dimensional data compared to score matching. Theoretically, we prove the consistency and asymptotic normality of sliced score matching estimators. Moreover, we demonstrate that sliced score matching can be used to learn deep score estimators for implicit distributions. In our experiments, we show sliced score matching can learn deep energy-based models effectively, and can produce accurate score estimates for applications such as variational inference with implicit distributions and training Wasserstein Auto-Encoders.

Key facts. Cited by 381 papers in the map (data through 7 Oct 2026). First posted on arXiv 17 May 2019.

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Citing papers per year: 2020: 2; 2021: 22; 2022: 50; 2023: 100; 2024: 99; 2025: 75; 2026: 33.

381 papers.

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