We introduce a diffusion-based cross-domain image translator in the absence of paired training data. Unlike GAN-based methods, our approach integrates diffusion models to learn the image translation process, allowing for more coverable modeling of the data distribution and performance improvement of the cross-domain translation. However, incorporating the translation process within the diffusion process is still challenging since the two processes are not aligned exactly, i.e., the diffusion process is applied to the noisy signal while the translation process is conducted on the clean signal. As a result, recent diffusion-based studies employ separate training or shallow integration to learn the two processes, yet this may cause the local minimal of the translation optimization, constraining the effectiveness of diffusion models. To address the problem, we propose a novel joint learning framework that aligns the diffusion and the translation process, thereby improving the global optimality. Specifically, we propose to extract the image components with diffusion models to represent the clean signal and employ the translation process with the image components, enabling an end-to-end joint learning manner. On the other hand, we introduce a time-dependent translation network to learn the complex translation mapping, resulting in effective translation learning and significant performance improvement. Benefiting from the design of joint learning, our method enables global optimization of both processes, enhancing the optimality and achieving improved fidelity and structural consistency. We have conducted extensive experiments on RGB$\leftrightarrow$RGB and diverse cross-modality translation tasks including RGB$\leftrightarrow$Edge, RGB$\leftrightarrow$Semantics and RGB$\leftrightarrow$Depth, showcasing better generative performances than the state of the arts.