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Score-based diffusion models (SBDMs) have achieved the SOTA FID results inunpaired image-to-image translation (I2I). However, we notice that existingmethods totally ignore the training data in the source domain, leading tosub-optimal solutions for unpaired I2I. To this end, we propose energy-guidedstochastic differential equations (EGSDE) that employs an energy functionpretrained on both the source and target domains to guide the inference processof a pretrained SDE for realistic and faithful unpaired I2I. Building upon twofeature extractors, we carefully design the energy function such that itencourages the transferred image to preserve the domain-independent featuresand discard domain-specific ones. Further, we provide an alternativeexplanation of the EGSDE as a product of experts, where each of the threeexperts (corresponding to the SDE and two feature extractors) solelycontributes to faithfulness or realism. Empirically, we compare EGSDE to alarge family of baselines on three widely-adopted unpaired I2I tasks under fourmetrics. EGSDE not only consistently outperforms existing SBDMs-based methodsin almost all settings but also achieves the SOTA realism results withoutharming the faithful performance. Furthermore, EGSDE allows for flexibletrade-offs between realism and faithfulness and we improve the realism resultsfurther (e.g., FID of 51.04 in Cat to Dog and FID of 50.43 in Wild to Dog onAFHQ) by tuning hyper-parameters. The code is available athttps://github.com/ML-GSAI/EGSDE.

EGSDE: Unpaired Image-to-Image Translation via Energy-Guided Stochastic Differential Equations