The prediction of information diffusion or cascade has attracted much attention over the last decade. Most cascade prediction works target on predicting cascade-level macroscopic properties such as the final size of a cascade. Existing microscopic cascade prediction models which focus on user-level modeling either make strong assumptions on how a user gets infected by a cascade or limit themselves to a specific scenario where "who infected whom" information is explicitly labeled. The strong assumptions oversimplify the complex diffusion mechanism and prevent these models from better fitting real-world cascade data. Also, the methods which focus on specific scenarios cannot be generalized to a general setting where the diffusion graph is unobserved. To overcome the drawbacks of previous works, we propose a Neural Diffusion Model (NDM) for general microscopic cascade prediction. NDM makes relaxed assumptions and employs deep learning techniques including attention mechanism and convolutional network for cascade modeling. Both advantages enable our model to go beyond the limitations of previous methods, better fit the diffusion data and generalize to unseen cascades. Experimental results on diffusion prediction task over four realistic cascade datasets show that our model can achieve a relative improvement up to 26% against the best performing baseline in terms of F1 score.