Deterministic flow models, such as rectified flows, offer a general framework for learning a deterministic transport map between two distributions, realized as the vector field for an ordinary differential equation (ODE). However, they are sensitive to model estimation and discretization errors and do not permit different samples conditioned on an intermediate state, limiting their application. We present a general method to turn the underlying ODE of such flow models into a family of stochastic differential equations (SDEs) that have the same marginal distributions. This method permits us to derive families of stochastic samplers, for fixed (e.g., previously trained) deterministic flow models, that continuously span the spectrum of deterministic and stochastic sampling, given access to the flow field and the score function. Our method provides additional degrees of freedom that help alleviate the issues with the deterministic samplers and empirically outperforms them. We empirically demonstrate advantages of our method on a toy Gaussian setup and on the large scale ImageNet generation task. Further, our family of stochastic samplers provide an additional knob for controlling the diversity of generation, which we qualitatively demonstrate in our experiments.
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