With the emergence of diffusion models as the frontline of generative models, many researchers have proposed molecule generation techniques using conditional diffusion models. However, due to the fundamental nature of a molecule, which carries highly entangled correlations within a small number of atoms and bonds, it becomes difficult for a model to connect raw data with the conditions when the conditions become more complex as natural language. To address this, here we present a novel latent diffusion model dubbed LDMol, which enables a natural text-conditioned molecule generation. Specifically, LDMol is composed of three building blocks: a molecule encoder that produces a chemically informative feature space, a natural language-conditioned latent diffusion model using a Diffusion Transformer (DiT), and an autoregressive decoder for molecule re. In particular, recognizing that multiple SMILES notations can represent the same molecule, we employ a contrastive learning strategy to extract the chemical informative feature space. LDMol not only beats the existing baselines on the text-to-molecule generation benchmark but is also capable of zero-shot inference with unseen scenarios. Furthermore, we show that LDMol can be applied to downstream tasks such as molecule-to-text retrieval and text-driven molecule editing, demonstrating its versatility as a diffusion model.