We propose Vec2Summ, a novel method for abstractive summarization that frames the task as semantic compression. Vec2Summ represents a document collection using a single mean vector in the semantic embedding space, capturing the central meaning of the corpus. To reconstruct fluent summaries, we perform embedding inversion -- decoding this mean vector into natural language using a generative language model. To improve reconstruction quality and capture some degree of topical variability, we introduce stochasticity by sampling from a Gaussian distribution centered on the mean. This approach is loosely analogous to bagging in ensemble learning, where controlled randomness encourages more robust and varied outputs. Vec2Summ addresses key limitations of LLM-based summarization methods. It avoids context-length constraints, enables interpretable and controllable generation via semantic parameters, and scales efficiently with corpus size -- requiring only $O(d + d^2)$ parameters. Empirical results show that Vec2Summ produces coherent summaries for topically focused, order-invariant corpora, with performance comparable to direct LLM summarization in terms of thematic coverage and efficiency, albeit with less fine-grained detail. These results underscore Vec2Summ's potential in settings where scalability, semantic control, and corpus-level abstraction are prioritized.