Papers › Learning Interpolations between Boltzmann Densities
Learning Interpolations between Boltzmann Densities
Bálint Máté, François Fleuret
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 fₜ of energy functions between the target energy f₁ and the energy function of a generalized Gaussian f₀(x) = ||x/σ||ₚᵖ. The interpolation of energy functions induces an interpolation of Boltzmann densities pₜ ∝e^(-fₜ) and we aim to find a time-dependent vector field Vₜ that transports samples along the family pₜ of densities. The condition of transporting samples along the family pₜ is equivalent to satisfying the continuity equation with Vₜ and pₜ = Zₜ⁻¹e^(-fₜ). Consequently, we optimize Vₜ and fₜ to satisfy this partial differential equation. We experimentally compare the proposed training objective to the reverse KL-divergence on Gaussian mixtures and on the Boltzmann density of a quantum mechanical particle in a double-well potential.
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