SEEDS: Exponential SDE Solvers for Fast High-Quality Sampling from Diffusion Models

A potent class of generative models known as Diffusion Probabilistic Models (DPMs) has become prominent. A forward diffusion process adds gradually noise to data, while a model learns to gradually denoise. Sampling from pre-trained DPMs is obtained by solving differential equations (DE) defined by the learnt model, a process which has shown to be prohibitively slow. Numerous efforts on speeding-up this process have consisted on crafting powerful ODE solvers. Despite being quick, such solvers do not usually reach the optimal quality achieved by available slow SDE solvers. Our goal is to propose SDE solvers that reach optimal quality without requiring several hundreds or thousands of NFEs to achieve that goal. In this work, we propose Stochastic Exponential Derivative-free Solvers (SEEDS), improving and generalizing Exponential Integrator approaches to the stochastic case on several frameworks. After carefully analyzing the formulation of exact solutions of diffusion SDEs, we craft SEEDS to analytically compute the linear part of such solutions. Inspired by the Exponential Time-Differencing method, SEEDS uses a novel treatment of the stochastic components of solutions, enabling the analytical computation of their variance, and contains high-order terms allowing to reach optimal quality sampling $\sim3$-$5\times$ faster than previous SDE methods. We validate our approach on several image generation benchmarks, showing that SEEDS outperforms or is competitive with previous SDE solvers. Contrary to the latter, SEEDS are derivative and training free, and we fully prove strong convergence guarantees for them.

Two-stream convolutional networks for end-to-end learning of self-driving cars

We propose a methodology to extend the concept of Two-Stream Convolutional Networks to perform end-to-end learning for self-driving cars with temporal cues. The system has the ability to learn spatiotemporal features by simultaneously mapping raw images and pre-calculated optical flows directly to steering commands. Although optical flows encode temporal-rich information, we found that 2D-CNNs are prone to capturing features only as spatial representations. We show how the use of Multitask Learning favors the learning of temporal features via inductive transfer from a shared spatiotemporal representation. Preliminary results demonstrate a competitive improvement of 30% in prediction accuracy and stability compared to widely used regression methods trained on the Comma.ai dataset.