How much private information do text embeddings reveal about the original text? We investigate the problem of embeddinginversion, reconstructing the full text represented in dense text embeddings. We frame the problem as controlled generation: generating text that, when reembedded, is close to a fixed point in latent space. We find that although a naïve model conditioned on the embedding performs poorly, a multi-step method that iteratively corrects and re-embeds text is able to recoveroftext inputs exactly. We train our model to decode text embeddings from two state-of-the-art embedding models, and also show that our model can recover important personal information (full names)  from a dataset of clinical notes.111Our code is available on Github:github.com/jxmorris12/vec2text.