Financial networks have been the object of intense quantitative analysis during the last few decades. Their structure and the dynamical processes on top of them are of utmost importance to understand the emergent collective behavior behind economic and financial crises. In this paper, we propose a stylized model to understand the "domino effect" of distress in client-supplier networks. We provide a theoretical analysis of the model, and we apply it to several synthetic networks and a real customer-supplier network, supplied by one of the largest banks in Europe. Besides, the proposed model allows us to investigate possible scenarios for the functioning of the financial distress propagation and to assess the economic health of the full network. The main novelty of this model is the combination of two stochastic terms: an additive noise, accounting by the capability of trading and paying obligations, and a multiplicative noise representing the variations of the market. Both parameters are crucial to determining the maximum default probability and the diffusion process characteristics.