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In modern quantum field theory and statistical physics, the expectation values of observables are represented as integrals over function space. In most interesting problems, such integrals can only be computed numerically using lattice approximations, where the functional integral is replaced by a finite-order integral. The resulting multidimensional integrals are computed using Markov chain Monte Carlo methods. Contemporary deep machine learning generative algorithms allow for a significant acceleration of Monte Carlo calculations. The talk will discuss the applications of generative models in quantum scalar field theory.