# Denoising Likelihood Score Matching for Conditional Score-based Data Generation

arXiv: https://arxiv.org/abs/2203.14206 · HTML: https://mlsanity.com/paper/2203.14206/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 23 references that are in the map.
- First posted on arXiv 27 Mar 2022.

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [A Note on the Inception Score](https://mlsanity.com/paper/1801.01973/) (2018)
- [Classification Accuracy Score for Conditional Generative Models](https://mlsanity.com/paper/1905.10887/) (2019)
- [Source Separation with Deep Generative Priors](https://mlsanity.com/paper/2002.07942/) (2020)

## Built on by (most cited first, 30 of 46)

- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Diffusion Model-Based Image Editing: A Survey](https://mlsanity.com/paper/2402.17525/) (2024)
- [Refining Generative Process with Discriminator Guidance in Score-based Diffusion Models](https://mlsanity.com/paper/2211.17091/) (2022)
- [One-Step Diffusion Distillation via Deep Equilibrium Models](https://mlsanity.com/paper/2401.08639/) (2023)
- [On the Design Fundamentals of Diffusion Models: A Survey](https://mlsanity.com/paper/2306.04542/) (2023)
- [Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Models](https://mlsanity.com/paper/2210.04872/) (2022)
- [Curriculum Direct Preference Optimization for Diffusion and Consistency Models](https://mlsanity.com/paper/2405.13637/) (2024)
- [Enhancing Diffusion-Based Image Synthesis with Robust Classifier Guidance](https://mlsanity.com/paper/2208.08664/) (2022)
- [MMDisCo: Multi-Modal Discriminator-Guided Cooperative Diffusion for Joint Audio and Video Generation](https://mlsanity.com/paper/2405.17842/) (2024)
- [Generalization through variance: how noise shapes inductive biases in diffusion models](https://mlsanity.com/paper/2504.12532/) (2025)
- [DisDet: Exploring Detectability of Backdoor Attack on Diffusion Models](https://mlsanity.com/paper/2402.02739/) (2024)
- [On Investigating the Conservative Property of Score-Based Generative Models](https://mlsanity.com/paper/2209.12753/) (2022)
- [Boomerang: Local sampling on image manifolds using diffusion models](https://mlsanity.com/paper/2210.12100/) (2022)
- [Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modeling](https://mlsanity.com/paper/2310.18123/) (2023)
- [Label-Noise Robust Diffusion Models](https://mlsanity.com/paper/2402.17517/) (2024)
- [DiFaReli++: Diffusion Face Relighting with Consistent Cast Shadows](https://mlsanity.com/paper/2304.09479/) (2023)
- [FOOGD: Federated Collaboration for Both Out-of-distribution Generalization and Detection](https://mlsanity.com/paper/2410.11397/) (2024)
- [Null-text Guidance in Diffusion Models is Secretly a Cartoon-style Creator](https://mlsanity.com/paper/2305.06710/) (2023)
- [Learning Continuous Exposure Value Representations for Single-Image HDR Reconstruction](https://mlsanity.com/paper/2309.03900/) (2023)
- [Structure-Guided Adversarial Training of Diffusion Models](https://mlsanity.com/paper/2402.17563/) (2024)
- [Transfer Learning for Diffusion Models](https://mlsanity.com/paper/2405.16876/) (2024)
- [LightsOut: Diffusion-based Outpainting for Enhanced Lens Flare Removal](https://mlsanity.com/paper/2510.15868/) (2025)
- [Stream-DiffVSR: Low-Latency Streamable Video Super-Resolution via Auto-Regressive Diffusion](https://mlsanity.com/paper/2512.23709/) (2025)
- [Training Energy-Based Normalizing Flow with Score-Matching Objectives](https://mlsanity.com/paper/2305.15267/) (2023)
- [MixBridge: Heterogeneous Image-to-Image Backdoor Attack through Mixture of Schr"odinger Bridges](https://mlsanity.com/paper/2505.08809/) (2025)
- [DiffAug: A Diffuse-and-Denoise Augmentation for Training Robust Classifiers](https://mlsanity.com/paper/2306.09192/) (2023)
- [Rethinking cluster-conditioned diffusion models for label-free image synthesis](https://mlsanity.com/paper/2403.00570/) (2024)
- [D-Cubed: Latent Diffusion Trajectory Optimisation for Dexterous Deformable Manipulation](https://mlsanity.com/paper/2403.12861/) (2024)
- [EDELINE: Enhancing Memory in Diffusion-based World Models via Linear-Time Sequence Modeling](https://mlsanity.com/paper/2502.00466/) (2025)
- [Guiding Noisy Label Conditional Diffusion Models with Score-based Discriminator Correction](https://mlsanity.com/paper/2508.19581/) (2025)

## Abstract (arXiv)

Many existing conditional score-based data generation methods utilize Bayes' theorem to decompose the gradients of a log posterior density into a mixture of scores. These methods facilitate the training procedure of conditional score models, as a mixture of scores can be separately estimated using a score model and a classifier. However, our analysis indicates that the training objectives for the classifier in these methods may lead to a serious score mismatch issue, which corresponds to the situation that the estimated scores deviate from the true ones. Such an issue causes the samples to be misled by the deviated scores during the diffusion process, resulting in a degraded sampling quality. To resolve it, we formulate a novel training objective, called Denoising Likelihood Score Matching (DLSM) loss, for the classifier to match the gradients of the true log likelihood density. Our experimental evidence shows that the proposed method outperforms the previous methods on both Cifar-10 and Cifar-100 benchmarks noticeably in terms of several key evaluation metrics. We thus conclude that, by adopting DLSM, the conditional scores can be accurately modeled, and the effect of the score mismatch issue is alleviated.