Stream-level flow matching with Gaussian processes
This work offers an incremental improvement to continuous normalizing flows for researchers working on generative models, particularly those dealing with time series data.
This paper extends conditional flow matching (CFM) by modeling latent stochastic paths, called "streams," with Gaussian process (GP) distributions. This approach reduces variance in the estimated marginal vector field, improving generated sample quality, and allows for linking correlated training data points.
Flow matching (FM) is a family of training algorithms for fitting continuous normalizing flows (CNFs). Conditional flow matching (CFM) exploits the fact that the marginal vector field of a CNF can be learned by fitting least-squares regression to the conditional vector field specified given one or both ends of the flow path. In this paper, we extend the CFM algorithm by defining conditional probability paths along ``streams'', instances of latent stochastic paths that connect data pairs of source and target, which are modeled with Gaussian process (GP) distributions. The unique distributional properties of GPs help preserve the ``simulation-free" nature of CFM training. We show that this generalization of the CFM can effectively reduce the variance in the estimated marginal vector field at a moderate computational cost, thereby improving the quality of the generated samples under common metrics. Additionally, adopting the GP on the streams allows for flexibly linking multiple correlated training data points (e.g., time series). We empirically validate our claim through both simulations and applications to image and neural time series data.