Accurate protein function prediction requires integrating heterogeneous intrinsic signals (e.g., sequence and structure) with noisy extrinsic contexts (e.g., protein-protein interactions and GO term annotations). However, two key challenges hinder effective fusion: (i) cross-modal distributional mismatch among embeddings produced by pre-trained intrinsic encoders, and (ii) noisy relational graphs of extrinsic data that degrade GNN-based information aggregation. We propose Diffused and Aligned Multi-modal Protein Embedding (DAMPE), a unified framework that addresses these through two core mechanisms. First, we propose Optimal Transport (OT)-based representation alignment that establishes correspondence between intrinsic embedding spaces of different modalities, effectively mitigating cross-modal heterogeneity. Second, we develop a Conditional Graph Generation (CGG)-based information fusion method, where a condition encoder fuses the aligned intrinsic embeddings to provide informative cues for graph reconstruction. Meanwhile, our theoretical analysis implies that the CGG objective drives this condition encoder to absorb graph-aware knowledge into its produced protein representations. Empirically, DAMPE outperforms or matches state-of-the-art methods such as DPFunc on standard GO benchmarks, achieving AUPR gains of 0.002-0.013 pp and Fmax gains 0.004-0.007 pp. Ablation studies further show that OT-based alignment contributes 0.043-0.064 pp AUPR, while CGG-based fusion adds 0.005-0.111 pp Fmax. Overall, DAMPE offers a scalable and theoretically grounded approach for robust multi-modal protein representation learning, substantially enhancing protein function prediction.