Learning representations on graphs is foundational for many downstream tasks, and its synergy with diffusion models has emerged as a promising direction. However, diffusion-based methods for heterogeneous graphs remain underexplored, confronting two principal challenges: (1) The presence of noise and structural heterogeneity in graphs makes it challenging to accurately capture semantic transitions among diverse relation types. (2) The isotropic Gaussian noise used in forward diffusion fails to reflect graphs' inherent semantics and structural anisotropy. To address these, we propose ARDiff, a novel framework that integrates residual diffusion with anisotropic noise for heterogeneous graph learning. Specifically, we propose a semantic residual diffusion mechanism that progressively refines node embeddings by orchestrating transitions from low-semantic (high-noise) to high-semantic (low-noise) relational contexts, thus enabling step-wise distillation of task-relevant information. In addition, to address the limitations of conventional diffusion, we introduce an anisotropic diffusion strategy: in the forward process, noise injection is oriented by structural and semantic priors; in the denoising step, a conditional diffusion mechanism is guided by a random walk encoding, enhancing both topological consistency and semantic alignment. Extensive evaluation on heterogeneous graph datasets demonstrates that ARDiff significantly surpasses current leading methods in link prediction and node classification, setting a new paradigm and benchmark in heterogeneous graph representation learning.