# Feature-guided score diffusion for sampling conditional densities

arXiv: https://arxiv.org/abs/2410.11646 · HTML: https://mlsanity.com/paper/2410.11646/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 28 references that are in the map.
- First posted on arXiv 15 Oct 2024.

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [Diffusion Autoencoders: Toward a Meaningful and Decodable Representation](https://mlsanity.com/paper/2111.15640/) (2021)
- [Diffusion Art or Digital Forgery? Investigating Data Replication in Diffusion Models](https://mlsanity.com/paper/2212.03860/) (2022)
- [Generalization in diffusion models arises from geometry-adaptive harmonic representations](https://mlsanity.com/paper/2310.02557/) (2023)
- [Dynamical Regimes of Diffusion Models](https://mlsanity.com/paper/2402.18491/) (2024)
- [Denoising Diffusion Autoencoders are Unified Self-supervised Learners](https://mlsanity.com/paper/2303.09769/) (2023)
- [Classifier-Free Guidance is a Predictor-Corrector](https://mlsanity.com/paper/2408.09000/) (2024)
- [Solving Linear Inverse Problems Using the Prior Implicit in a Denoiser](https://mlsanity.com/paper/2007.13640/) (2020)
- [SODA: Bottleneck Diffusion Models for Representation Learning](https://mlsanity.com/paper/2311.17901/) (2023)
- [Diffusion-Based Representation Learning](https://mlsanity.com/paper/2105.14257/) (2021)
- [InfoDiffusion: Representation Learning Using Information Maximizing Diffusion Models](https://mlsanity.com/paper/2306.08757/) (2023)
- [What does guidance do? A fine-grained analysis in a simple setting](https://mlsanity.com/paper/2409.13074/) (2024)
- [Theoretical Insights for Diffusion Guidance: A Case Study for Gaussian Mixture Models](https://mlsanity.com/paper/2403.01639/) (2024)

## Built on by (most cited first, 3 of 3)

- [Generalization of Diffusion Models Arises with a Balanced Representation Space](https://mlsanity.com/paper/2512.20963/) (2025)
- [When and how can inexact generative models still sample from the data manifold?](https://mlsanity.com/paper/2508.07581/) (2025)
- [MCLR: Improving Conditional Modeling via Inter-Class Likelihood-Ratio Maximization and Unifying Classifier-Free Guidance with Alignment Objectives](https://mlsanity.com/paper/2603.22364/) (2026)

## Abstract (arXiv)

Score diffusion methods can learn probability densities from samples. The score of the noise-corrupted density is estimated using a deep neural network, which is then used to iteratively transport a Gaussian white noise density to a target density. Variants for conditional densities have been developed, but correct estimation of the corresponding scores is difficult. We avoid these difficulties by introducing an algorithm that guides the diffusion with a projected score. The projection pushes the image feature vector towards the feature vector centroid of the target class. The projected score and the feature vectors are learned by the same network. Specifically, the image feature vector is defined as the spatial averages of the channels activations in select layers of the network. Optimizing the projected score for denoising loss encourages image feature vectors of each class to cluster around their centroids. It also leads to the separations of the centroids. We show that these centroids provide a low-dimensional Euclidean embedding of the class conditional densities. We demonstrate that the algorithm can generate high quality and diverse samples from the conditioning class. Conditional generation can be performed using feature vectors interpolated between those of the training set, demonstrating out-of-distribution generalization.