Following [2], we extend our method into multi-domain translation on AFHQ dataset, where the source domain includes Cat and Wild and the target domain is Dog. In this setting, similar to two-domain unpaired I2I, the EGSDE also employs an energy function pretrained on both the source and target domains to guide the inference process of a pretrained SDE. The only difference is the domain-specific feature extractor Es(,) involved in the energy function is the all but the last eliminate layer of randomness.

Score-based diffusion models (SBDMs) have achieved the SOTAFID results in unpaired image-to-image translation (I2I). However, we notice that existing methods totally ignore the training data in the source domain, leading to sub-optimal solutions for unpaired I2I. To this end, we propose energy-guided stochastic differential equations (EGSDE) that employs an energy function pretrained on both the source and target domains to guide the inference process of a pretrained SDE for realistic and faithful unpaired I2I. Building upon two feature extractors, we carefully design the energy function such that it encourages the transferred image to preserve the domain-independent features and discard domain-specific ones. Further, we provide an alternative explanation of the EGSDE as a product of experts, where each of the three experts (corresponding to the SDE and two feature extractors) solely contributes to faithfulness or realism. Empirically, we compare EGSDE to a large family of baselines on three widely-adopted unpaired I2I tasks under four metrics. EGSDE not only consistently outperforms existing SBDMs-based methods in almost all settings but also achieves the SOTA realism results without harming the faithful performance. Furthermore, EGSDE allows for flexible trade-offs between realism and faithfulness and we improve the realism results further (e.g., FID of 51.04 in Cat Dog and FID of 50.43 in Wild Dog on AFHQ) by tuning hyper-parameters. The code is available at https://github.com/ML-GSAI/EGSDE.

Unpaired image-to-image translation (I2I) aims to transfer an image from a source domain to a related targetdomain, whichinvolvesawide range ofcomputer vision tasks such asstyle transfer, super-resolution and pose estimation [35]. InI2I, the translated image should berealistictofitthe style of the target domain by changing the domain-specific features accordingly, andfaithful to preservethedomain-independent featuresofthesourceimage.

Score-based diffusion models (SBDMs) have achieved the SOTA FID results in unpaired image-to-image translation (I2I). However, we notice that existing methods totally ignore the training data in the source domain, leading to sub-optimal solutions for unpaired I2I. To this end, we propose energy-guided stochastic differential equations (EGSDE) that employs an energy function pretrained on both the source and target domains to guide the inference process of a pretrained SDE for realistic and faithful unpaired I2I. Building upon two feature extractors, we carefully design the energy function such that it encourages the transferred image to preserve the domain-independent features and discard domain-specific ones. Further, we provide an alternative explanation of the EGSDE as a product of experts, where each of the three experts (corresponding to the SDE and two feature extractors) solely contributes to faithfulness or realism. Empirically, we compare EGSDE to a large family of baselines on three widely-adopted unpaired I2I tasks under four metrics. EGSDE not only consistently outperforms existing SBDMs-based methods in almost all settings but also achieves the SOTA realism results without harming the faithful performance. Furthermore, EGSDE allows for flexible trade-offs between realism and faithfulness and we improve the realism results further (e.g., FID of 51.04 in Cat $\to$ Dog and FID of 50.43 in Wild $\to$ Dog on AFHQ) by tuning hyper-parameters. The code is available at https://github.com/ML-GSAI/EGSDE.

Score-based diffusion models (SBDMs) have achieved the SOTA FID results in unpaired image-to-image translation (I2I). However, we notice that existing methods totally ignore the training data in the source domain, leading to sub-optimal solutions for unpaired I2I. To this end, we propose energy-guided stochastic differential equations (EGSDE) that employs an energy function pretrained on both the source and target domains to guide the inference process of a pretrained SDE for realistic and faithful unpaired I2I. Building upon two feature extractors, we carefully design the energy function such that it encourages the transferred image to preserve the domain-independent features and discard domain-specific ones. Further, we provide an alternative explanation of the EGSDE as a product of experts, where each of the three experts (corresponding to the SDE and two feature extractors) solely contributes to faithfulness or realism. Empirically, we compare EGSDE to a large family of baselines on three widely-adopted unpaired I2I tasks under four metrics.