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However, the unavoidable discreteness of a molecule makes it difficult for a diffusion model to connect raw data with highly complex conditions like natural language. To address this, we present a novel latent diffusion model dubbed LDMol for text-conditioned molecule generation. LDMol comprises a molecule autoencoder that produces a learnable and structurally informative feature space, and a natural language-conditioned latent diffusion model. In particular, recognizing that multiple SMILES notations can represent the same molecule, we employ a contrastive learning strategy to extract feature space that is aware of the unique characteristics of the molecule structure. LDMol outperforms the existing baselines on the text-to-molecule generation benchmark, suggesting a potential for diffusion models can outperform autoregressive models in text data generation with a better choice of the latent domain. 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