Naive neural dialogue generation models tend to produce repetitive and dull utterances. The promising adversarial models train the generator against a well-designed discriminator to push it to improve towards the expected direction. However, assessing dialogues requires consideration of many aspects of linguistics, which are difficult to be fully covered by a single discriminator. To address it, we reframe the dialogue generation task as a multi-objective optimization problem and propose a novel adversarial dialogue generation framework with multiple discriminators that excel in different objectives for multiple linguistic aspects, called AMPGAN, whose feasibility is proved by theoretical derivations. Moreover, we design an adaptively adjusted sampling distribution to balance the discriminators and promote the overall improvement of the generator by continuing to focus on these objectives that the generator is not performing well relatively. Experimental results on two real-world datasets show a significant improvement over the baselines.