| Summary: | Significant progress has been made in the field of deep generative models, with notable examples such as ChatGPT and image-generation tools like Midjourney, Stable Diffusion, and DALL·E showcasing remarkable performance. One of the key mathematical models behind these advancements is denoising diffusion models (DDMs, Ho et al., 2020; Song et al., 2021), which belong to a class of generative models aiming to reconstruct clean data from noisy observations. DDMs have demonstrated significant effectiveness in diverse applications, including image restoration, image inpainting, and generative modelling.
In this project, our focus will be on a systematic study of denoising diffusion models and their integration with geometric representations for molecular generation. In general, DDMs operate by iteratively transforming noisy observed data towards a desired clean state through a series of diffusion steps. Each diffusion step involves updating the data using a diffusion process that gradually reduces the noise level. This process is typically guided by a learnable diffusion model that determines the transition probabilities for transforming the data at each step. Additionally, geometric models offer a more intrinsic and informative representation for molecules. By combining geometric representations with DDMs, we can explore the generation of various types of molecules. Overall, this project aims to investigate denoising diffusion models comprehensively and explore their synergy with geometric representations in the context of molecular generation.
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