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Trajectory crossing remains a critical bottleneck in Flow Matching (FM), and previous works typically view these crossings from a theoretical optimization perspective causing velocity averaging. They attempt to address it indirectly by post-hoc distillation or endpoint coupling, without explicitly regulating the interm...
A novel guided method is proposed by using the h-transform, a tool that can constrain stochastic processes (e.g., sampling process) under desired conditions and modify the transition probability at each sampling timestep by adding to the original differential equation with a drift function, which approximately steers t...
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