  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 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.
