Accurate protein function prediction remains a fundamental challenge in bioinformatics, requiring computational methods that effectively translate amino acid sequences into functional annotations. We present DeepGO-ESM, a graph-based model that leverages the Evolutionary Scale Modeling (ESM) framework to improve protein function prediction based on the architecture of DeepGraphGO. In our approach, ESM transforms protein sequences into semantic embeddings, which are then utilized in two complementary graph-based prediction scenarios: a homogeneous protein-protein interaction graph where edges are directly inferred from embedding similarities, and a heterogeneous graph that integrates proteins with the directed acyclic structure of Gene Ontology terms. Through rigorous benchmark evaluations against other computational methods, our method demonstrates better predictive performance across multiple assessment metrics, particularly in scenarios with limited annotation data. Furthermore, our heterogeneous graph-based approach outperforms both conventional graph-based methods and state-of-the-art non-graph sequence models. The key innovations of DeepGO-ESM lie in: i) the automatic derivation of protein-protein interaction networks directly from ESM-generated embeddings, eliminating reliance on pre-existing interaction databases, and ii) the development of dual prediction models operating on both homogeneous protein graphs and heterogeneous protein-GO term networks. These contributions establish DeepGO-ESM as a powerful paradigm that bridges deep sequence modeling with structured biological knowledge, advancing computational approaches to functional genomics.