# Target Score Matching

arXiv: https://arxiv.org/abs/2402.08667 · HTML: https://mlsanity.com/paper/2402.08667/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 24 of its 33 references that are in the map.
- First posted on arXiv 13 Feb 2024.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

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

- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Riemannian Score-Based Generative Modelling](https://mlsanity.com/paper/2202.02763/) (2022)
- [SE(3) diffusion model with application to protein backbone generation](https://mlsanity.com/paper/2302.02277/) (2023)
- [Path Integral Sampler: a stochastic control approach for sampling](https://mlsanity.com/paper/2111.15141/) (2021)
- [Denoising Diffusion Samplers](https://mlsanity.com/paper/2302.13834/) (2023)
- [Riemannian Diffusion Models](https://mlsanity.com/paper/2208.07949/) (2022)
- [Iterated Denoising Energy Matching for Sampling from Boltzmann Densities](https://mlsanity.com/paper/2402.06121/) (2024)
- [Improved sampling via learned diffusions](https://mlsanity.com/paper/2307.01198/) (2023)
- [Let us Build Bridges: Understanding and Extending Diffusion Generative Models](https://mlsanity.com/paper/2208.14699/) (2022)
- [Non-Denoising Forward-Time Diffusions](https://mlsanity.com/paper/2312.14589/) (2023)
- [Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics](https://mlsanity.com/paper/2302.00600/) (2023)
- [Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimization](https://mlsanity.com/paper/2310.02679/) (2023)
- [Bayesian Learning via Neural Schr"odinger-F"ollmer Flows](https://mlsanity.com/paper/2111.10510/) (2021)
- [Reverse Diffusion Monte Carlo](https://mlsanity.com/paper/2307.02037/) (2023)
- [Scaling Riemannian Diffusion Models](https://mlsanity.com/paper/2310.20030/) (2023)
- [Renormalizing Diffusion Models](https://mlsanity.com/paper/2308.12355/) (2023)
- [Generative Diffusion Models for Lattice Field Theory](https://mlsanity.com/paper/2311.03578/) (2023)
- [A Wasserstein Minimum Velocity Approach to Learning Unnormalized Models](https://mlsanity.com/paper/2002.07501/) (2020)

## Built on by (most cited first, 30 of 50)

- [Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts](https://mlsanity.com/paper/2503.02819/) (2025)
- [Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matching](https://mlsanity.com/paper/2504.11713/) (2025)
- [Schr"odinger Bridge Flow for Unpaired Data Translation](https://mlsanity.com/paper/2409.09347/) (2024)
- [Consistent Diffusion Meets Tweedie: Training Exact Ambient Diffusion Models with Noisy Data](https://mlsanity.com/paper/2404.10177/) (2024)
- [Scalable Equilibrium Sampling with Sequential Boltzmann Generators](https://mlsanity.com/paper/2502.18462/) (2025)
- [Steering Masked Discrete Diffusion Models via Discrete Denoising Posterior Prediction](https://mlsanity.com/paper/2410.08134/) (2024)
- [Accelerated Diffusion Models via Speculative Sampling](https://mlsanity.com/paper/2501.05370/) (2025)
- [No Trick, No Treat: Pursuits and Challenges Towards Simulation-free Training of Neural Samplers](https://mlsanity.com/paper/2502.06685/) (2025)
- [Progressive Inference-Time Annealing of Diffusion Models for Sampling from Boltzmann Densities](https://mlsanity.com/paper/2506.16471/) (2025)
- [Target Concrete Score Matching: A Holistic Framework for Discrete Diffusion](https://mlsanity.com/paper/2504.16431/) (2025)
- [Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Models](https://mlsanity.com/paper/2506.17139/) (2025)
- [Training Neural Samplers with Reverse Diffusive KL Divergence](https://mlsanity.com/paper/2410.12456/) (2024)
- [Adjoint Schr"odinger Bridge Sampler](https://mlsanity.com/paper/2506.22565/) (2025)
- [RNE: plug-and-play diffusion inference-time control and energy-based training](https://mlsanity.com/paper/2506.05668/) (2025)
- [FEAT: Free energy Estimators with Adaptive Transport](https://mlsanity.com/paper/2504.11516/) (2025)
- [Proximal Diffusion Neural Sampler](https://mlsanity.com/paper/2510.03824/) (2025)
- [Variational Distillation of Diffusion Policies into Mixture of Experts](https://mlsanity.com/paper/2406.12538/) (2024)
- [Density Ratio Estimation with Conditional Probability Paths](https://mlsanity.com/paper/2502.02300/) (2025)
- [Progressive Tempering Sampler with Diffusion](https://mlsanity.com/paper/2506.05231/) (2025)
- [Amortized Sampling with Transferable Normalizing Flows](https://mlsanity.com/paper/2508.18175/) (2025)
- [Diffusion Models in Simulation-Based Inference: A Tutorial Review](https://mlsanity.com/paper/2512.20685/) (2025)
- [Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matching](https://mlsanity.com/paper/2603.00530/) (2026)
- [Markovian Flow Matching: Accelerating MCMC with Continuous Normalizing Flows](https://mlsanity.com/paper/2405.14392/) (2024)
- [Learned Reference-based Diffusion Sampling for multi-modal distributions](https://mlsanity.com/paper/2410.19449/) (2024)
- [Solvation Free Energies from Neural Thermodynamic Integration](https://mlsanity.com/paper/2410.15815/) (2024)
- [Hamiltonian Score Matching and Generative Flows](https://mlsanity.com/paper/2410.20470/) (2024)
- [Control Variate Score Matching for Diffusion Models](https://mlsanity.com/paper/2512.20003/) (2025)
- [Flow Sampling: Learning to Sample from Unnormalized Densities via Denoising Conditional Processes](https://mlsanity.com/paper/2605.03984/) (2026)
- [Markov Chain Monte Carlo with Diffusion Paths](https://mlsanity.com/paper/2607.11631/) (2026)
- [Sampling from multi-modal distributions with polynomial query complexity in fixed dimension via reverse diffusion](https://mlsanity.com/paper/2501.00565/) (2024)

## Abstract (arXiv)

Denoising Score Matching estimates the score of a noised version of a target distribution by minimizing a regression loss and is widely used to train the popular class of Denoising Diffusion Models. A well known limitation of Denoising Score Matching, however, is that it yields poor estimates of the score at low noise levels. This issue is particularly unfavourable for problems in the physical sciences and for Monte Carlo sampling tasks for which the score of the clean original target is known. Intuitively, estimating the score of a slightly noised version of the target should be a simple task in such cases. In this paper, we address this shortcoming and show that it is indeed possible to leverage knowledge of the target score. We present a Target Score Identity and corresponding Target Score Matching regression loss which allows us to obtain score estimates admitting favourable properties at low noise levels.