Video Latent Flow Matching: Optimal Polynomial Projections for Video Interpolation and Extrapolation
Yang Cao, Zhao Song, Chiwun Yang
TL;DR
This work addresses efficient text-to-video generation by modeling a time-varying flow of latent patches through a caption-guided process. It combines a bijective visual decoder with HiPPO-LegS polynomial projections and Flow Matching to produce a time-dependent latent flow that can be interpolated and extrapolated at arbitrary frame rates. The approach is backed by theory: universal approximation via Diffusion Transformer (DiT) and error bounds for interpolation/extrapolation, along with timescale robustness to sampling. Empirically, VLFM (with Stable Diffusion as the visual decoder and DiT-XL-2 as backbone) demonstrates strong text-to-video generation, interpolation, and extrapolation across seven large-scale datasets, offering an efficient and flexible pathway for real-world video synthesis.
Abstract
This paper considers an efficient video modeling process called Video Latent Flow Matching (VLFM). Unlike prior works, which randomly sampled latent patches for video generation, our method relies on current strong pre-trained image generation models, modeling a certain caption-guided flow of latent patches that can be decoded to time-dependent video frames. We first speculate multiple images of a video are differentiable with respect to time in some latent space. Based on this conjecture, we introduce the HiPPO framework to approximate the optimal projection for polynomials to generate the probability path. Our approach gains the theoretical benefits of the bounded universal approximation error and timescale robustness. Moreover, VLFM processes the interpolation and extrapolation abilities for video generation with arbitrary frame rates. We conduct experiments on several text-to-video datasets to showcase the effectiveness of our method.