UC San Diego Researchers DYffusion: A Dynamics-Based Diffusion Model for Spatiotemporal Forecasting

Projecting the future behavior of a dynamical system, or forecasting its dynamics, involves understanding the underlying dynamics that drive the evolution of the system to make accurate predictions about its future states. Accurate and reliable probabilistic projections are crucial for risk management, resource optimization, policy development and strategic planning. In many applications it is very difficult to generate accurate long-term probabilistic predictions. Techniques used in operational contexts typically rely on complex numerical models that require supercomputers to complete calculations in reasonable time periods, often sacrificing grid spatial resolution.

An interesting approach to forecasting probabilistic dynamics is generative modeling. Natural distributions of images and videos can be modeled effectively using, in particular, diffusion models. Gaussian diffusion is the typical method; through the “forward process”, it corrupts the data to varying degrees with Gaussian noise, and through the “reverse process”, it systematically removes noise from a random input at the time of inference to generate extremely realistic samples. However, in high dimensions, learning to map from noise to genuine data is difficult, particularly when data is sparse. As a result, training and finalizing diffusion models requires prohibitively high computing costs, requiring a sequential sampling procedure through hundreds of diffusion stages.

For example, sampling 50,000 32×32 photographs using a diffusion denoising probabilistic model (DDPM) takes approximately 20 hours. Furthermore, not many techniques use diffusion models that go beyond static images. While video diffusion models are capable of producing realistic samples, they do not specifically use the temporal aspect of the data to produce accurate projections. In this study, researchers at the University of California, San Diego present a new framework for multi-step probabilistic forecasting that trains a dynamics-informed diffusion model. They provide a novel breakthrough process motivated by recent discoveries demonstrating the possibilities of non-Gaussian diffusion processes. To carry out this procedure, a time-conditioned neural network is used, which depends on temporal interpolation.

Their method imposes an inductive bias by linking the time steps in the dynamical system to the phases of the diffusion process without requiring assumptions about the physical system. As a result, the computational complexity of your diffusion model decreases with respect to memory usage, data efficiency, and the number of diffusion steps required for training. For high-dimensional spatiotemporal data, their resulting framework based on diffusion models, which they refer to as DYffusion, naturally captures long-range relationships and produces accurate probabilistic ensemble predictions.

Below is a summary of his contributions:

• From the point of view of diffusion models, they study probabilistic spatiotemporal prediction and its applicability to complex physical systems with many dimensions and few data.

• They provide DYffusion, an adaptive framework that uses inductive temporal bias to shorten learning times and reduce memory requirements for multi-step forecasting and long-term perspectives. DYffusion is an implicit model that learns the solutions of a dynamical system, and cold sampling can be interpreted as the solution of the Euler method.

• They also conduct an empirical study comparing the computational requirements and performance of state-of-the-art probabilistic methods, including conditional video diffusion models, in dynamic forecasting. Finally, they explore the theoretical implications of their method. They find that, compared to conventional Gaussian diffusion, the suggested process produces good probabilistic predictions and increases computational efficiency.

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