Diffusion models enable high-quality virtual try-on (VTO) with their established image synthesis abilities. Despite the extensive end-to-end training of large pre-trained models involved in current VTO methods, real-world applications often prioritize limited training and inference, serving, and deployment budgets for VTO. To solve this obstacle, we apply Doob's h-transform efficient fine-tuning (DEFT) for adapting large pre-trained unconditional models for downstream image-conditioned VTO abilities. DEFT freezes the pre-trained model's parameters and trains a small h-transform network to learn a conditional h-transform. The h-transform network allows training only 1.42 percent of the frozen parameters, compared to a baseline of 5.52 percent in traditional parameter-efficient fine-tuning (PEFT). To further improve DEFT's performance and decrease existing models' inference time, we additionally propose an adaptive consistency loss. Consistency training distills slow but high-performing diffusion models into a fast one while retaining performance by enforcing consistencies along the inference path. Inspired by constrained optimization, instead of distillation, we combine the consistency loss and the denoising score matching loss in a data-adaptive manner for fine-tuning existing VTO models at a low cost. Empirical results show the proposed DEFT-VTON method achieves state-of-the-art performance on VTO tasks, with as few as 15 denoising steps, while maintaining competitive results.