(Communicated by Xinmin Yang) Abstract: In this paper, we concentrate on a broad class of large-scale nonconvex and nonsmooth optimization problems. We first propose a novel inertial stochastic Bregman proximal alternating linearized minimization algorithm (TiSBPALM), which employs variance-reduced stochastic gradient estimators. Subsequently, under the assumption that the objective function satisfies the Kurdyka-Łojasiewicz property and certain conditions on the parameters are imposed, we prove that the sequence generated by our algorithm converges to a critical point in expectation. Additionally, we provide the convergence rate for the iteration sequence. Finally, we conduct numerical experiments on sparse nonnegative matrix factorization and blind image-deblurring to verify the effectiveness of our proposed algorithms.