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Details of Grant 

EPSRC Reference: EP/Y018273/1
Title: Theory for Denoising Diffusion Models: generalisation and sample complexity
Principal Investigator: DELIGIANNIDIS, Professor G
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Statistics
Organisation: University of Oxford
Scheme: New Investigator Award
Starts: 31 May 2024 Ends: 30 May 2027 Value (£): 524,406
EPSRC Research Topic Classifications:
Non-linear Systems Mathematics Statistics & Appl. Probability
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
20 Nov 2023 EPSRC Mathematical Sciences Small Grants and Prioritisation Panel November 2023 Announced
Summary on Grant Application Form
Modern society is faced with an abundance of data, ranging from audio, images, and videos captured on our smartphones to massive datasets containing social media networks and medical information for millions of patients. One of the primary objectives of artificial intelligence (AI) is to design systems that can recognize patterns and extract meaning from such datasets, a task at which humans excel.

Generative modelling, an active topic in machine learning and AI, aims to learn how to generate new samples from an unknown distribution, having access only to samples from that distribution.

Generative models have numerous applications, including anomaly detection, lossless compression, generating realistic images with specific features, filling in missing parts or improving the resolution of images captured by cameras on our phones. Generative models are also routinely used as scientific tools by researchers working on drug discovery, protein structure discovery, molecular design, medical imaging and many more disciplines.

Perhaps the best known example of a generative model is the recent ChatGPT (Generative Pre-trained Transformer) chatbot. ChatGPT is a highly sophisticated generative model that can

hold realistic conversations and even write computer code!

In the past decade, generative modelling has made tremendous progress, largely due to advancements in neural networks and deep learning. While several key algorithms have emerged, until recently, the most successful approach thus far has been Generative Adversarial Networks (GANs). In fact GANs remained the best approach until the recent emergence of Score-based Generative Models (SGMs), specifically Denoising Diffusion Models (DDMs). DDMs are now the dominant class of generative models, achieving state-of-the-art results in many applications, including image generation. DDMs are routinely used to generate text, audio, solve inverse problems, medical imaging, and even for protein structure discovery. The tremendous success and popularity of these models has generated a critical need to comprehend their statistical properties and their ability to generate new samples from unknown target distributions. Despite recent advancements we presently lack a precise explanation for the observed empirical success of these models.

The goal of this project is to bridge this gap in our understanding and develop a theoretical framework that underpins the success of DDMs. With the expanding influence of AI, particularly generative models, on contemporary society, this project is timely and holds significant potential for making a profound impact in academia and beyond.
Key Findings
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Potential use in non-academic contexts
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