Multi-interest candidate matching plays a pivotal role in personalized recommender systems, as it captures diverse user interests from their historical behaviors. Most existing methods utilize attention mechanisms to generate interest representations by aggregating historical item embeddings. However, these methods only capture overall item-level relevance, leading to coarse-grained interest representations that include irrelevant information. To address this issue, we propose the Diffusion Multi-Interest model (DMI), a novel framework for refining user interest representations at the dimension level. Specifically, DMI first introduces controllable noise into coarse-grained interest representations at the dimensional level. Then, in the iterative reconstruction process, DMI combines a cross-attention mechanism and an item pruning strategy to reconstruct the personalized interest vectors with the guidance of tailored collaborative information. Extensive experiments demonstrate the effectiveness of DMI, surpassing state-of-the-art methods on offline evaluations and an online A/B test. Successfully deployed in the real-world recommender system, DMI effectively enhances user satisfaction and system performance at scale, serving the major traffic of hundreds of millions of daily active users. \footnote{The code will be released for reproducibility once the paper is accepted.}