# Risk-Sensitive Diffusion: Robustly Optimizing Diffusion Models with Noisy Samples

arXiv: https://arxiv.org/abs/2402.02081 · HTML: https://mlsanity.com/paper/2402.02081/

## Key facts

- Cited by 1 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 61 references that are in the map.
- First posted on arXiv 3 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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [NoMaD: Goal Masked Diffusion Policies for Navigation and Exploration](https://mlsanity.com/paper/2310.07896/) (2023)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [Ambient Diffusion: Learning Clean Distributions from Corrupted Data](https://mlsanity.com/paper/2305.19256/) (2023)
- [DALL-E-Bot: Introducing Web-Scale Diffusion Models to Robotics](https://mlsanity.com/paper/2210.02438/) (2022)
- [MDM: Molecular Diffusion Model for 3D Molecule Generation](https://mlsanity.com/paper/2209.05710/) (2022)
- [MissDiff: Training Diffusion Models on Tabular Data with Missing Values](https://mlsanity.com/paper/2307.00467/) (2023)
- [Automatic Text Evaluation through the Lens of Wasserstein Barycenters](https://mlsanity.com/paper/2108.12463/) (2021)
- [A Review of Deep Learning Methods for Irregularly Sampled Medical Time Series Data](https://mlsanity.com/paper/2010.12493/) (2020)
- [Conformal Prediction with Missing Values](https://mlsanity.com/paper/2306.02732/) (2023)
- [Personalized Risk Scoring for Critical Care Prognosis using Mixtures of Gaussian Processes](https://mlsanity.com/paper/1610.08853/) (2016)

## Built on by (most cited first, 1 of 1)

- [Learning Robust Diffusion Models from Imprecise Supervision](https://mlsanity.com/paper/2510.03016/) (2025)

## Abstract (arXiv)

Diffusion models are mainly studied on image data. However, non-image data (e.g., tabular data) are also prevalent in real applications and tend to be noisy due to some inevitable factors in the stage of data collection, degrading the generation quality of diffusion models. In this paper, we consider a novel problem setting where every collected sample is paired with a vector indicating the data quality: risk vector. This setting applies to many scenarios involving noisy data and we propose risk-sensitive SDE, a type of stochastic differential equation (SDE) parameterized by the risk vector, to address it. With some proper coefficients, risk-sensitive SDE can minimize the negative effect of noisy samples on the optimization of diffusion models. We conduct systematic studies for both Gaussian and non-Gaussian noise distributions, providing analytical forms of risk-sensitive SDE. To verify the effectiveness of our method, we have conducted extensive experiments on multiple tabular and time-series datasets, showing that risk-sensitive SDE permits a robust optimization of diffusion models with noisy samples and significantly outperforms previous baselines.