Title: Learning Latent Topology for Graph Matching. Abstract: Graph matching (GM) has been traditionally modeled as a deterministic optimization problem characterized by an affinity matrix under pre-defined graph topology. Though there have been several attempts on learning more effective node-level affinity/representation for matching, they still heavily rely on the initial graph structure/topology which is typically obtained through heuristic ways (e.g. Delauney or $k$-nearest) and will not be adjusted during the learning process to adapt to problem-specific patterns. We argue that a standalone graph representation learning is insufficient for GM task, whereby a GM solver may favor some latent topology other than pre-defined one. Motivated by this hypothesis, we propose to learn latent graph topology in replacement of the fixed topology as input. To this end, we devise two types of latent graph generation procedures in deterministic and generative fashion, respectively. Particularly, the generative procedure emphasizes the across-graph consistency and thus can be viewed as a \textbf{co-generative} model. Our methods show superior performance over previous state-of-the-arts on several benchmarks, thus strongly supporting our hypothesis.