Deformable image registration aims to precisely align medical images from different modalities or times. Traditional deep learning methods, while effective, often lack interpretability, real-time observability and adjustment capacity during registration inference. Denoising diffusion models present an alternative by reformulating registration as iterative image denoising. However, existing diffusion registration approaches do not fully harness capabilities, neglecting the critical sampling phase that enables continuous observability during the inference. Hence, we introduce DiffuseReg, an innovative diffusion-based method that denoises deformation fields instead of images for improved transparency. We also propose a novel denoising network upon Swin Transformer, which better integrates moving and fixed images with diffusion time step throughout the denoising process. Furthermore, we enhance control over the denoising registration process with a novel similarity consistency regularization. Experiments on ACDC datasets demonstrate DiffuseReg outperforms existing diffusion registration methods by 1.32 in Dice score. The sampling process in DiffuseReg enables real-time output observability and adjustment unmatched by previous deep models.