Using neural networks for supervised learning means learning a function that maps input x to output y .However, in many applications, the inverse learning is also wanted, i.e. , inferring y from x , which requires invertibility of the learning.Since the dimension of input is usually much higher than that of the output, there is information loss in the forward learning from input to output.Thus, creating invertible neural networks is a difficult task.However, recent development of invertible learning techniques such as normalizing flows has made invertible neural networks a reality.In this work, we applied flow-based invertible neural networks as generative models to inverse mol. design.In this context, the forward learning is to predict chem. properties given a mol., and the inverse learning is to infer the mols. given the chem. properties.Trained on 100 and 1000 mols., resp., from a benchmark dataset QM9, our model identified novel mols. that had chem. property values well exceeding the limits of the training mols. as well as the limits of the whole QM9 of 133,885 mols., moreover our generative model could easily sample many mols. (x values) from any one chem. property value (y value).Compared with the previous method in the literature that could only optimize one mol. for one chem. property value at a time, our model could be trained once and then be sampled any multiple times and for any chem. property values without the need of retraining.This advantage comes from treating inverse mol. design as an inverse regression problem.In summary, our main contributions were two: 1) our model could generalize well from the training data and was very data efficient, 2) our model could learn bidirectional correspondence between mols. and their chem. properties, thereby offering the ability to sample any number of mols. from any y values.In conclusion, our findings revealed the efficiency and effectiveness of using invertible neural networks as generative models in inverse mol. design.