Transfer learning of diffusion models to smaller target domains is challenging, as naively fine-tuning the model often results in poor generalization. Test-time guidance methods help mitigate this by offering controllable improvements in image fidelity through a trade-off with sample diversity. However, this benefit comes at a high computational cost, typically requiring dual forward passes during sampling. We propose the \underline{Do}main-\underline{g}uided \underline{Fi}ne-\underline{t}uning (DogFit) method, an effective guidance mechanism for diffusion transfer learning that maintains controllability without incurring additional computational overhead. DogFit injects a domain-aware guidance offset into the training loss, effectively internalizing the guided behavior during the fine-tuning process. The domain-aware design is motivated by our observation that during fine-tuning, the unconditional source model offers a stronger marginal estimate than the target model. To support efficient controllable fidelity–diversity trade-offs at inference, we encode the guidance strength value as an additional model input through a lightweight conditioning mechanism. We further investigate the optimal placement and timing of the guidance offset during training and propose two simple scheduling strategies, i.e., \textit{late-start} and \textit{cut-off}, which improve generation quality and training stability. Experiments \footnote{Code is provided in suppl. materials and will be made public.} on DiT and SiT backbones across six diverse target domains show that DogFit can outperform prior guidance methods in transfer learning in terms of FID and $\text{FD}_{\text{DINOV2}}$ while requiring up to 2× fewer sampling TFLOPS.