Learning Deformation Trajectories of Boltzmann Densities

01/18/2023

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by   Bálint Máté, et al.

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We introduce a training objective for continuous normalizing flows that can be used in the absence of samples but in the presence of an energy function. Our method relies on either a prescribed or a learnt interpolation f_t of energy functions between the target energy f_1 and the energy function of a generalized Gaussian f_0(x) = |x/σ|^p. This, in turn, induces an interpolation of Boltzmann densities p_t ∝ e^-f_t and we aim to find a time-dependent vector field V_t that transports samples along this family of densities. Concretely, this condition can be translated to a PDE between V_t and f_t and we minimize the amount by which this PDE fails to hold. We compare this objective to the reverse KL-divergence on Gaussian mixtures and on the ϕ^4 lattice field theory on a circle.