This paper introduces Target Score Matching (TSM), a novel approach to estimate the score of a target distribution by leveraging knowledge of the score of the "clean" target. Denoising Score Matching (DSM) is a widely used method for training Denoising Diffusion Models, but it suffers from poor performance at low noise levels. The authors address this limitation by presenting a Target Score Identity (TSI) and corresponding TSM loss that allow for more accurate score estimation at low noise levels. The TSI leverages the known score of the clean target to improve the estimation of the score of the noisy version of the target. The TSM loss is derived from the TSI and is shown to have favorable properties at low noise levels compared to DSM. The paper also discusses extensions of TSI and TSM to non-additive noise models, Lie groups, and bridge matching. Experiments show that TSM outperforms DSM in terms of variance and accuracy, particularly for low noise levels. The results demonstrate that TSM provides a more stable and accurate estimation of the score, making it a promising approach for applications in generative modeling and other areas where score estimation is important.This paper introduces Target Score Matching (TSM), a novel approach to estimate the score of a target distribution by leveraging knowledge of the score of the "clean" target. Denoising Score Matching (DSM) is a widely used method for training Denoising Diffusion Models, but it suffers from poor performance at low noise levels. The authors address this limitation by presenting a Target Score Identity (TSI) and corresponding TSM loss that allow for more accurate score estimation at low noise levels. The TSI leverages the known score of the clean target to improve the estimation of the score of the noisy version of the target. The TSM loss is derived from the TSI and is shown to have favorable properties at low noise levels compared to DSM. The paper also discusses extensions of TSI and TSM to non-additive noise models, Lie groups, and bridge matching. Experiments show that TSM outperforms DSM in terms of variance and accuracy, particularly for low noise levels. The results demonstrate that TSM provides a more stable and accurate estimation of the score, making it a promising approach for applications in generative modeling and other areas where score estimation is important.