  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.
