  Samplers are the backbone of the implementations of any randomised algorithm.
Unfortunately, obtaining an efficient algorithm to test the correctness of
samplers is very hard to find. Recently, in a series of works, testers like
$\mathsf{Barbarik}$, $\mathsf{Teq}$, $\mathsf{Flash}$ for testing of some
particular kinds of samplers, like CNF-samplers and Horn-samplers, were
obtained. But their techniques have a significant limitation because one can
not expect to use their methods to test for other samplers, such as perfect
matching samplers or samplers for sampling linear extensions in posets. In this
paper, we present a new testing algorithm that works for such samplers and can
estimate the distance of a new sampler from a known sampler (say, uniform
sampler). Testing the identity of distributions is the heart of testing the
correctness of samplers. This paper's main technical contribution is developing
a new distance estimation algorithm for distributions over high-dimensional
cubes using the recently proposed sub-cube conditioning sampling model. Given
subcube conditioning access to an unknown distribution $P$, and a known
distribution $Q$ defined over $\{0,1\}^n$, our algorithm
$\mathsf{CubeProbeEst}$ estimates the variation distance between $P$ and $Q$
within additive error $\zeta$ using $O\left({n^2}/{\zeta^4}\right)$ subcube
conditional samples from $P$. Following the testing-via-learning paradigm, we
also get a tester which distinguishes between the cases when $P$ and $Q$ are
$\varepsilon$-close or $\eta$-far in variation distance with probability at
least $0.99$ using $O({n^2}/{(\eta-\varepsilon)^4})$ subcube conditional
samples. The estimation algorithm in the sub-cube conditioning sampling model
helps us to design the first tester for self-reducible samplers.
