Guiding diffusion generative models with applications to inverse problems

Conditional sampling via denoising diffusion models (DDMs) has received significant interest in generative modelling for their scalability, improved sample quality, and versatile application. These models are widely used in scientific and industrial settings, where they leverage latent representations of data and complex relationships that span different data modalities. In some of these applications, there is a known mathematical relationship that maps latent variables to observed data, requiring the recovery of latent variables from observed data – an inverse problem. Treating both the latent variable and the data as realisations of random variables, we aim to sample a probability distribution that assigns a probability to each possible solution for a latent signal x, given the observed data y, known as the posterior, p(x|y). DDMs targeting p(x) are repurposed for solving inverse problems by using Bayes rule as a mapping from p(x) to the posterior p(x|y). Existing approaches, known as guidance methods, use Gaussian approximations to the conditional densities via Tweedie’s formula to parameterise the mean, and are complemented by various heuristics. We make two contributions to the improvement of methodology for solving inverse problems via the use of generative priors. The first contribution is to address challenges from these approximations by incorporating higher-order information via Tweedie’s formula for a statistically principled approximation. We present a theoretical guarantee specific to posterior sampling. This contributes to a deeper theoretical understanding of diffusion-guided sampling. We demonstrate the empirical effectiveness of our method on general linear inverse problems, using both synthetic examples and image restoration tasks. In our second contribution, we investigate a novel application of conditional generation in construction planning services, in collaboration with our industry partner, nPlan. Using DDMs, we leverage text data from construction project schedules to estimate activity durations within a schedule generation pipeline. Additionally, we quantify risk by applying statistical regression models to predict construction activity delays. Transforming delay prediction into an ordinal regression task, we compare the performance of a Multilayer Perceptron (MLP) model with that of Gaussian Processes. Our findings suggest that the MLP model is better suited for this task, highlighting potential for future work on delay distribution modeling.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2025

Author dc:creator

• Boys, Benjamin

Advisors dc:contributor.advisor

• Girolami, Mark
• Akyildiz, Özgen Deniz

• AI

Licence

• https://www.repository.cam.ac.uk/bitstreams/bad767a3-f995-4dc3-8ab6-d61200131175/download
• http://purl.org/NET/rdflicense/allrightsreserved

Language dc:language

eng

Author Identifier

0000-0001-7078-2720

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/393542