Image Generation with langevin dynamics (2024)
In the field of machine learning, Diffusion Probabilistic Models have emerged as a prominent category of generative models. Their main objective is to learn a diffusion process that describes the probability distribution of a given dataset. The essence of diffusion-based generative models finds its roots in statistical physics, where diffusion is modeled by describing the Brownian motion of particles through a physical system. Inspired by these concepts, diffusion generative models adopt diffusion as a central process. By understanding how data diffuse in an abstract space, these models capture inherent patterns and generate synthetic data that reflects the underlying structure of real datasets. This study undertakes a comparative analysis between Denoising Diffusion Probabilistic Models and statistical physics. It was discovered that the “diffusion” process of data, as elucidated in the seminal paper by Jo et al. (2020), can be effectively explained using a specialized version of the Langevin Equation. Building upon this understanding and leveraging the work of Song et al. on score-based generative modeling through stochastic differential equations, we expanded the framework of DPMs by examining continuous time diffusion processes, as opposed to the discrete time framework presented by Jo et al. This continuous time perspective provided deeper insights into the physical principles underlying DPMs. Furthermore, it facilitated new observations and advancements in the development of DPMs, enhancing our comprehension and application of these models.