Title: An Information Fusion Approach to Learning with Instance-Dependent Label Noise. Abstract: Instance-dependent label noise (IDN) widely exists in real-world datasets and usually misleads the training of deep neural networks. Noise transition matrix (NTM) (i.e., the probability that clean labels flip into noisy labels) is used to characterize the label noise and can be adopted to bridge the gap between clean and noisy underlying data distributions. However, most instances are long-tail, i.e., the number of occurrences of each instance is usually limited, which leads to the gap between the underlying distribution and the empirical distribution. Therefore, the genuine problem caused by IDN is \emph{empirical}, instead of underlying, \emph{data distribution mismatch} during training. To directly tackle the empirical distribution mismatch problem, we propose \emph{posterior transition matrix} (PTM) to posteriorly model label noise given limited observed noisy labels, which achieves \emph{statistically consistent classifiers}. Note that even if an instance is corrupted by the same NTM, the intrinsic randomness incurs different noisy labels, and thus requires different correction methods. Motivated by this observation, we propose an \textbf{I}nformation \textbf{F}usion (IF) approach to fine-tune the NTM based on the estimated PTM. Specifically, we adopt the noisy labels and model predicted probabilities to estimate the PTM and then correct the NTM in \emph{forward propagation}. Empirical evaluations on synthetic and real-world datasets demonstrate that our method is superior to the state-of-the-art approaches, and achieves more stable training for instance-dependent label noise. 