The ability to leverage images from co-available modalities to inform target-domain reconstruction is highly desirable in imaging algorithms. In this work, we introduce Generative Translation Priors (GTP)--a Bayesian framework that transforms diffusion-based image-to-image translation models into cross-modality image priors for ill-posed imaging inverse problems. GTP incorporates target-domain measurements through likelihood guidance, steering the translation process toward the desired posterior distribution. The framework is grounded in a theoretical analysis of the resulting posterior dynamics, which reveals an intrinsic bias introduced by likelihood guidance. We further characterize this bias and derive a ground-truth-free formulation for its estimation, enabling it to serve as a practical metric for assessing posterior sampling quality. Building on this analysis, we derive two discretized GTP algorithms based on gradient and proximal likelihood guidance, respectively. We validate GTP on computed tomography reconstruction with magnetic resonance side information, and on positron emission tomography reconstruction with computed tomography side information. Experiments demonstrate that GTP effectively incorporates complementary cross-modality information and achieves high-fidelity reconstruction even under severely undersampled measurements.

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