# Conffusion: Confidence Intervals for Diffusion Models

arXiv: https://arxiv.org/abs/2211.09795 · HTML: https://mlsanity.com/paper/2211.09795/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 33 of its 39 references that are in the map.
- First posted on arXiv 17 Nov 2022.

## Placed in

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

## Builds on (most cited first, 30 of 33)

- [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)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (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)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [An Image is Worth One Word: Personalizing Text-to-Image Generation using Textual Inversion](https://mlsanity.com/paper/2208.01618/) (2022)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Blended Diffusion for Text-driven Editing of Natural Images](https://mlsanity.com/paper/2111.14818/) (2021)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Exploring the Limits of Weakly Supervised Pretraining](https://mlsanity.com/paper/1805.00932/) (2018)
- [Diffusion Autoencoders: Toward a Meaningful and Decodable Representation](https://mlsanity.com/paper/2111.15640/) (2021)
- [ResNeSt: Split-Attention Networks](https://mlsanity.com/paper/2004.08955/) (2020)
- [Blended Latent Diffusion](https://mlsanity.com/paper/2206.02779/) (2022)
- [SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Models](https://mlsanity.com/paper/2104.14951/) (2021)
- [Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction](https://mlsanity.com/paper/2112.05146/) (2021)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)

## Built on by (most cited first, 30 of 33)

- [Break-A-Scene: Extracting Multiple Concepts from a Single Image](https://mlsanity.com/paper/2305.16311/) (2023)
- [Dreamix: Video Diffusion Models are General Video Editors](https://mlsanity.com/paper/2302.01329/) (2023)
- [Conformal Language Modeling](https://mlsanity.com/paper/2306.10193/) (2023)
- [The Chosen One: Consistent Characters in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2311.10093/) (2023)
- [Towards Coherent Image Inpainting Using Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2304.03322/) (2023)
- [Conformal Prediction for Deep Classifier via Label Ranking](https://mlsanity.com/paper/2310.06430/) (2023)
- [How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Control](https://mlsanity.com/paper/2302.03791/) (2023)
- [On the Posterior Distribution in Denoising: Application to Uncertainty Quantification](https://mlsanity.com/paper/2309.13598/) (2023)
- [Principal Uncertainty Quantification with Spatial Correlation for Image Restoration Problems](https://mlsanity.com/paper/2305.10124/) (2023)
- [Conformal Contextual Robust Optimization](https://mlsanity.com/paper/2310.10003/) (2023)
- [Uncertainty Quantification via Neural Posterior Principal Components](https://mlsanity.com/paper/2309.15533/) (2023)
- [From Posterior Sampling to Meaningful Diversity in Image Restoration](https://mlsanity.com/paper/2310.16047/) (2023)
- [Conformal Generative Modeling with Improved Sample Efficiency through Sequential Greedy Filtering](https://mlsanity.com/paper/2410.01660/) (2024)
- [Task-Driven Uncertainty Quantification in Inverse Problems via Conformal Prediction](https://mlsanity.com/paper/2405.18527/) (2024)
- [PSC: Posterior Sampling-Based Compression](https://mlsanity.com/paper/2407.09896/) (2024)
- [C-Adapter: Adapting Deep Classifiers for Efficient Conformal Prediction Sets](https://mlsanity.com/paper/2410.09408/) (2024)
- [X-Diffusion: Generating Detailed 3D MRI Volumes From a Single Image Using Cross-Sectional Diffusion Models](https://mlsanity.com/paper/2404.19604/) (2024)
- [Spatial-Aware Conformal Prediction for Trustworthy Hyperspectral Image Classification](https://mlsanity.com/paper/2409.01236/) (2024)
- [Statistical Methods in Generative AI](https://mlsanity.com/paper/2509.07054/) (2025)
- [Uncertainty Visualization via Low-Dimensional Posterior Projections](https://mlsanity.com/paper/2312.07804/) (2023)
- [Ultrasound Imaging based on the Variance of a Diffusion Restoration Model](https://mlsanity.com/paper/2403.15316/) (2024)
- [Metric-Guided Conformal Bounds for Probabilistic Image Reconstruction](https://mlsanity.com/paper/2404.15274/) (2024)
- [Diffusion Reconstruction of Ultrasound Images with Informative Uncertainty](https://mlsanity.com/paper/2310.20618/) (2023)
- [Conformal Bounds on Full-Reference Image Quality for Imaging Inverse Problems](https://mlsanity.com/paper/2505.09528/) (2025)
- [Singleton-Optimized Conformal Prediction](https://mlsanity.com/paper/2509.24095/) (2025)
- [How Good Are Deep Generative Models for Solving Inverse Problems?](https://mlsanity.com/paper/2312.12691/) (2023)
- [Segmentation-Guided CT Synthesis with Pixel-Wise Conformal Uncertainty Bounds](https://mlsanity.com/paper/2503.08515/) (2025)
- [Towards Distribution-Shift Uncertainty Estimation for Inverse Problems with Generative Priors](https://mlsanity.com/paper/2510.10947/) (2025)
- [Minimax Multi-Target Conformal Prediction with Applications to Imaging Inverse Problems](https://mlsanity.com/paper/2511.13533/) (2025)
- [Empirical Bayes Conformal Prediction for Vision and Language Models](https://mlsanity.com/paper/2605.23189/) (2026)

## Abstract (arXiv)

Diffusion models have become the go-to method for many generative tasks, particularly for image-to-image generation tasks such as super-resolution and inpainting. Current diffusion-based methods do not provide statistical guarantees regarding the generated results, often preventing their use in high-stakes situations. To bridge this gap, we construct a confidence interval around each generated pixel such that the true value of the pixel is guaranteed to fall within the interval with a probability set by the user. Since diffusion models parametrize the data distribution, a straightforward way of constructing such intervals is by drawing multiple samples and calculating their bounds. However, this method has several drawbacks: i) slow sampling speeds ii) suboptimal bounds iii) requires training a diffusion model per task. To mitigate these shortcomings we propose Conffusion, wherein we fine-tune a pre-trained diffusion model to predict interval bounds in a single forward pass. We show that Conffusion outperforms the baseline method while being three orders of magnitude faster.