Abstract visual reasoning (AVR) enables humans to quickly discover and generalize abstract rules to new scenarios. Designing intelligent systems with human-like AVR abilities has been a long-standing topic in the artificial intelligence community. Deep AVR solvers have recently achieved remarkable success in various AVR tasks. However, they usually use task-specific designs or parameters in different tasks. In such a paradigm, solving new tasks often means retraining the model, and sometimes retuning the model architectures, which increases the cost of solving AVR problems. In contrast to task-specific approaches, this paper proposes a novel Unified Conditional Generative Solver (UCGS), aiming to address multiple AVR tasks in a unified framework. First, we prove that some well-known AVR tasks can be reformulated as the problem of estimating the predictability of target images in problem panels. Then, we illustrate that, under the proposed framework, training one conditional generative model can solve various AVR tasks. The experiments show that with a single round of multi-task training, UCGS demonstrates abstract reasoning ability across various AVR tasks. Especially, UCGS exhibits the ability of zero-shot reasoning, enabling it to perform abstract reasoning on problems from unseen AVR tasks in the testing phase.