Building Normalizing Flows with Stochastic Interpolants
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A simple generative model based on a continuous-time normalizing flow between any pair of base and target distributions is proposed. The velocity field of this flow is inferred from the probability current of a time-dependent distribution that interpolates between the base and the target in finite time. Unlike conventional normalizing flow inference methods based the maximum likelihood principle, which require costly backpropagation through ODE solvers, our interpolant approach leads to a simple quadratic loss for the velocity itself which is expressed in terms of expectations that are readily amenable to empirical estimation. The flow can be used to generate samples from either the base or target, and can be used to estimate the likelihood at any time along the interpolant. The approach is contextualized in its relation to diffusions. In particular, in situations where the base is a Gaussian distribution, we show that the velocity of our normalizing flow can also be used to construct a diffusion model to sample the target as well as estimating its score. This allows one to map methods based on stochastic differential equations to those of ordinary differential equations, simplifying the mechanics of the model, but capturing equivalent dynamics. Benchmarking on density estimation tasks illustrates that the learned flow can match and surpass maximum likelihood continuous flows at a fraction of the conventional ODE training costs.
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