Title: Efficient Controllable Generation with Guarantee. Abstract: Generative models have achieved great success in image synthesis, and controllability of the generative process is a key requirement for their successful adoption in real-world applications. Most existing methods for controllable generation lack theoretical guarantees and are time-consuming, which weakens their reliability and applicability. In this paper, we propose an identifiability theorem to provide a guarantee of controllability. This theorem ensures that semantic attributes can be disentangled and hence independently controlled by orthogonalization in latent space in a supervised manner. Based on the theoretical analysis, we propose a general method for controllable generation, which can be integrated with most latent-variable generative models. We further propose to plug it into a pre-trained NVAE. Such a scheme significantly reduces the cost of time and has better consistency in image editing due to the merits of NVAE. Experiments show that our method is comparable with the state-of-the-art methods in attribute-conditional generation and image editing, and has advantages in efficiency and consistency.