A key challenge towards the goal of multi-part assembly tasks is finding robust sensorimotor control methods in the presence of uncertainty. In contrast to previous works that rely on a priori knowledge on whether two parts match, we aim to learn this through physical interaction. We propose a hierarchical approach that enables a robot to autonomously assemble parts while being uncertain about part types and positions. In particular, our probabilistic approach learns a set of differentiable filters that leverage the tactile sensorimotor trace from failed assembly attempts to update its belief about part position and type. This enables a robot to overcome assembly failure. We demonstrate the effectiveness of our approach on a set of object fitting tasks. The experimental results indicate that our proposed approach achieves higher precision in object position and type estimation, and accomplishes object fitting tasks faster than baselines.