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As a post-processing procedure, the diffusion process has demonstrated its ability of substantially improving the performance of various visual retrieval systems. Whereas, great efforts are also devoted to similarity (or metric) fusion, seeing that only one individual type of similarity cannot fully reveal the intrinsic relationship between objects. This stimulates a great research interest of considering similarity fusion in the framework of the diffusion process (i.e., fusion with diffusion) for robust retrieval. In this paper, we first revisit representative methods about fusion with diffusion and provide new insights which are ignored by previous researchers. Then, observing that existing algorithms are susceptible to noisy similarities, the proposed regularized ensemble diffusion (RED) is bundled with an automatic weight learning paradigm, so that the negative impacts of noisy similarities are suppressed. Though formulated as a convex optimization problem, one advantage of RED is that it converts back into the iteration-based solver with the same computational complexity as the conventional diffusion process. At last, we integrate several recently-proposed similarities with the proposed framework. The experimental results suggest that we can achieve new state-of-the-art performances on various retrieval tasks, including 3D shape retrieval on the ModelNet data set, and image retrieval on the Holidays and Ukbench data sets. [ABSTRACT FROM AUTHOR]