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.
