For SGMCMC the output is usually biased samples, so how to do this? One idea is to consider the fullbatch version and use a small step size (so the sampler is now an unadjusted langevin sampler). You can then test whether the samples are good (using a Kernel GoF test for example).
How to do integration tests for SGMCMC algorithms?
For MCMC, one standard approach is Simulation Based Calibration which is used in several PPLs (Stan or Rainer). Another approach is to use Kernel goodness of fit test which for some reason is not really used in practice.
For SGMCMC the output is usually biased samples, so how to do this? One idea is to consider the fullbatch version and use a small step size (so the sampler is now an unadjusted langevin sampler). You can then test whether the samples are good (using a Kernel GoF test for example).