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Recently, diffusion models have been extensively studied as powerful generative tools for image translation. However, the existing diffusion model-based image translation approaches often suffer from several limitations: 1) slow inference due to iterative denoising, 2) the necessity for paired training data, or 3) constraints from learning only one-way translation paths. To mitigate these limitations, here we introduce a novel framework, called Implicit Bridge Consistency Distillation (IBCD), that extends consistency distillation with a diffusion implicit bridge model that connects PF-ODE trajectories from any distribution to another one. Moreover, to address the challenges associated with distillation errors from consistency distillation, we introduce two unique improvements: Distribution Matching for Consistency Distillation (DMCD) and distillation-difficulty adaptive weighting method. Experimental results confirm that IBCD for bidirectional translation can achieve state-of-the-art performance on benchmark datasets in just one step generation.