We introduce a new functional representation for 3D molecules based on their continuous atomic density fields. Using this representation, we propose a new model based on neural empirical Bayes for unconditional 3D molecule generation in the continuous space using neural fields. Our model, FuncMol, encodes molecular fields into latent codes using a conditional neural field, samples noisy codes from a Gaussian-smoothed distribution with Langevin MCMC, denoises these samples in a single step and finally decodes them into molecular fields. FuncMol performs all-atom generation of 3D molecules without assumptions on the molecular structure and scales well with the size of molecules, unlike most existing approaches. Our method achieves competitive results on drug-like molecules and easily scales to macro-cyclic peptides, with at least one order of magnitude faster sampling. The code is available at https://github.com/prescient-design/funcmol.