This paper addresses the problem of inferring link loss rates based on network performance tomography in noisy network systems. Since network tomography emerged, all existing tomography-based methods are limited to the fulfillment of a basic condition: both network topologies and end-to-end routes must be absolutely accurate, which in most cases is impractical, especially for large-scale heterogeneous networks. To overcome the impracticability of tomography-based methods, we propose a robust tomography-based loss inference method capable of accurately inferring all link loss rates even when the given knowledge about the system is unreliable. Rather than computing the link loss rates directly from end-to-end loss rates, it calculates an upper bound for each link loss rate. It then infers all the link loss rates that most closely conform to the measurement results within their upper bounds. For a scenario where noisy measurements are caused by link (or router port) failures, we propose a hidden fault diagnosis approach that utilizes the inferred link loss rates to pinpoint the insidious faults that are hardly detected. It first determines the possible fake routes based on inferred link loss rates. Subsequently, it finds the maximum probable faults that can best explain the fake routes. Through intensive experiments, the results strongly confirm the promising performance of our proposed approaches.