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We propose a new method for simulating lattice gauge theories in the presenceof fermions. The method combines flow-based generative models for local gaugefield updates and hierarchical updates of the factorized fermion determinant.The flow-based generative models are restricted to proposing updates togauge-fields within subdomains, thus keeping training times moderate whileincreasing the global volume. We apply our method performs to the 2-dimensional(2D) Schwinger model with $N_f=2$ Wilson Dirac fermions and show that nocritical slowing down is observed in the sampling of topological sectors up to$\beta=8.45$. Furthermore, we show that fluctuations can be suppressedexponentially with the distance between active subdomains, allowing us toachieve acceptance rates of up to $99\%$ for the outer-most accept/reject stepon lattices volumes of up to $V=128\times128$.

Tackling critical slowing down using global correction steps with equivariant flows: the case of the Schwinger model