operator implemented by a combinational stochastic circuit. Each stochastic transition circuit is $T_{S|X}$ is parameterized by some input $X$, and its internal combinational stochastic block $P(S_{t+1}|S_t,X)$ must ergodically converge to a unique stationary distribution $P(S|X)$ for all $X$. (C) Stochastic transition circuits can be composed to construct samplers for probabilistic models over multiple variables by wiring together stochastic transition circuits for each variable based on their interactions. This circuit samples from a distribution $P(A,B,C) = P(A)P(B|A)P(C|A)$. (D) Each network of stochastic transition circuits can be scheduled in many ways; here we show one serial schedule and one parallel schedule for the transition circuit from (C). Convergence depends only on respecting the invariant that no stochastic transition circuit transitions while other circuits that interact with it are transitioning. (E) The Markov chain implemented by this transition circuit. (F) Typical stochastic evolutions of the state in this circuit. (G) Inference can be implemented by clamping state variables to specific values; this yields a restricted Markov chain that converges to the conditional distribution over the unclamped variables given the clamped ones. Here we show the chain obtained by fixing $C=1$. (H) Typical stochastic evolutions of the state in this clamped transition circuit. Changing 