Neural Architecture Search (NAS) methods often suffer from low search efficiency since they have to explore a large and complex architecture search space. To accelerate the architecture search, generative methods learn a search space capturing intricate architecture distributions and generate promising architectures guided by a strong predictor within the latent space. However, since the architecture space is often exponentially large and highly non-convex, even a very strong predictor model is difficult in fitting the whole space, which may degrade their performance. To address this problem, this paper proposes a novel framework named Progressive Neural Architecture Generation with Weaker Predictors (WeakPNAG), which uses conditional diffusion models to generate promising architectures guided by weak predictors. Different from existing generative NAS methods which use a single strong predictor, our WeakPNAG progressively shrinks the sample space based on predictions from previous weak predictors, and updates new weak predictors towards the subspace of better architectures. In this way, our WeakPNAG iteratively learns to generate samples from increasingly promising latent subspaces. Extensive experiments on standard benchmarks demonstrate that our WeakPNAG achieves superior performance with reduced evaluation time compared with SOTA NAS methods.