We describe a general recipe for constructing Metropolis updates for Diagrammatic Monte-Carlo
(DiagMC) algorithms, based on the Schwinger-Dyson equations in quantum field theory. This
approach bypasses explicit duality transformations, enumeration or classification of diagrams and
can be used for lattice quantum field theories with unknown or complicated dual representations
(such as non-Abelian lattice gauge theories). DiagMC algorithms constructed in this way can still
be plagued by the sign problem, which is, however, completely different from the sign problem in
conventional Monte-Carlo simulations and has its origin in cancellations between diagrams with
positive and negative weights. To test the presented approach, we apply DiagMC to calculate
the first 7 orders of $1/N^2$ expansion in the quartic matrix model and find good agreement with
analytic results, with the exception of the close vicinity of the critical coupling where the critical
slowing down sets in.