mlsanityData to 14 Oct 2026

Score Matching With Missing Data

arXiv 2506.00557 ↗First posted 31 May 2025stat.ML cs.LG stat.MEcited by 8

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Abstract (arXiv)

Score matching is a vital tool for learning the distribution of data with applications across many areas including diffusion processes, energy based modelling, and graphical model estimation. Despite all these applications, little work explores its use when data is incomplete. We address this by adapting score matching (and its major extensions) to work with missing data in a flexible setting where data can be partially missing over any subset of the coordinates. We provide two separate score matching variations for general use, an importance weighting (IW) approach, and a variational approach. We provide finite sample bounds for our IW approach in finite domain settings and show it to have especially strong performance in small sample lower dimensional cases. Complementing this, we show our variational approach to be strongest in more complex high-dimensional settings which we demonstrate on graphical model estimation tasks on both real and simulated data.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 23 of its 31 references that are in the map. First posted on arXiv 31 May 2025.

Builds on

23 of 31 references.

References · 23

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  2. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  3. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 672
  4. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 582
  5. 2015Importance Weighted Autoencoderscited by 456
  6. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 384
  7. 2018GAIN: Missing Data Imputation using Generative Adversarial Netscited by 352
  8. 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matchingcited by 183
  9. 2023Ambient Diffusion: Learning Clean Distributions from Corrupted Datacited by 111
  10. 2023MissDiff: Training Diffusion Models on Tabular Data with Missing Valuescited by 39
  11. 2020MCFlow: Monte Carlo Flow Models for Data Imputationcited by 37
  12. 2019Learning Energy-Based Models in High-Dimensional Spaces with Multi-scale Denoising Score Matchingcited by 26
11 more
  1. 2015Estimation of High-Dimensional Graphical Models Using Regularized Score Matchingcited by 20
  2. 2019Estimating Density Models with Truncation Boundaries using Score Matchingcited by 20
  3. 2020Generalized Score Matching for General Domainscited by 13
  4. 2017Graphical Lasso and Thresholding: Equivalence and Closed-form Solutionscited by 12
  5. 2020Bi-level Score Matching for Learning Energy-based Latent Variable Modelscited by 10
  6. 2020Variational (Gradient) Estimate of the Score Function in Energy-based Latent Variable Modelscited by 8
  7. 2018Graphical Models for Non-Negative Data Using Generalized Score Matchingcited by 6
  8. 2017Learning Deep Energy Models: Contrastive Divergence vs. Amortized MLEcited by 5
  9. 2014Clustering via Mode Seeking by Direct Estimation of the Gradient of a Log-Densitycited by 3
  10. 2015Robust Gaussian Graphical Modeling with the Trimmed Graphical Lassocited by 3
  11. 2019Imputation estimators for unnormalized models with missing datacited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 5.

8 papers.

  1. 2026AutoSOTA: An End-to-End Automated Research System for State-of-the-Art AI Model Discoverycited by 23
  2. 2025Incomplete Data, Complete Dynamics: A Diffusion Approachcited by 3
  3. 2026AugMask: Training Diffusion Models on Incomplete Tabular Data via Stochastic Augmentation and Maskingcited by 1
  4. 2025Smooth Flow Matching for Synthesizing Functional Datacited by 0
  5. 2025Learning Robust Diffusion Models from Imprecise Supervisioncited by 0
  6. 2026Latent Diffusion for Missing Datacited by 0
  7. 2026Flow Matching with Missing Datacited by 0
  8. 2026Learning Field Reconstruction from Incomplete Data by Globally Correcting Local Estimatescited by 0