This paper introduces a novel approach to speech restoration by integrating a context-related conditioning strategy. Specifically, we employ the diffusion-based generative restoration model, UNIVERSE++, as a backbone to evaluate the effectiveness of contextual representations. We incorporate acoustic context embeddings extracted from the CLAP model, which capture the environmental attributes of input audio. Additionally, we propose an Acoustic Context (ACX) representation that refines CLAP embeddings to better handle various distortion factors and their intensity in speech signals. Unlike content-based approaches that rely on linguistic and speaker attributes, ACX provides contextual information that enables the restoration model to distinguish and mitigate distortions better. Experimental results indicate that context-aware conditioning improves both restoration performance and its stability across diverse distortion conditions, reducing variability compared to content-based methods.