User attributes, such as gender and education, face severe incompleteness in social networks. In order to make this kind of valuable data usable for downstream tasks like user profiling and personalized recommendation, attribute inference aims to infer users' missing attribute labels based on observed data. Recently, variational autoencoder (VAE), an end-to-end deep generative model, has shown promising performance by handling the problem in a semi-supervised way. However, VAEs can easily suffer from over-fitting and over-smoothing when applied to attribute inference. To be specific, VAE implemented with multi-layer perceptron (MLP) can only reconstruct input data but fail in inferring missing parts. While using the trending graph neural networks (GNNs) as encoder has the problem that GNNs aggregate redundant information from neighborhood and generate indistinguishable user representations, which is known as over-smoothing. In this paper, we propose an attribute \textbf{Infer}ence model based on \textbf{A}dversarial \textbf{VAE} (Infer-AVAE) to cope with these issues. Specifically, to overcome over-smoothing, Infer-AVAE unifies MLP and GNNs in encoder to learn positive and negative latent representations respectively. Meanwhile, an adversarial network is trained to distinguish the two representations and GNNs are trained to aggregate less noise for more robust representations through adversarial training. Finally, to relieve over-fitting, mutual information constraint is introduced as a regularizer for decoder, so that it can make better use of auxiliary information in representations and generate outputs not limited by observations. We evaluate our model on 4 real-world social network datasets, experimental results demonstrate that our model averagely outperforms baselines by 7.0$\%$ in accuracy.