The success of foundation AI has motivated the research of circuit foundation models, which are customized to assist the integrated circuit (IC) design process. However, existing pre-trained circuit models are typically limited to standalone encoders for predictive tasks or decoders for generative tasks. These two model types are developed independently, operate on different circuit modalities, and reside in separate latent spaces, which restricts their ability to complement each other for more advanced applications. In this work, we present GenEDA, the first framework that aligns circuit encoders with decoders within a shared latent space. GenEDA bridges the gap between graph-based circuit representations and text-based large language models (LLMs), enabling communication between their respective latent spaces. To achieve the alignment, we propose two paradigms that support both open-source trainable LLMs and commercial frozen LLMs. Built on this aligned architecture, GenEDA enables three unprecedented generative reasoning tasks over netlists, where the model reversely generates the high-level functionality from low-level netlists in different granularities. These tasks extend traditional gate-type prediction to direct generation of full-circuit functionality. Experiments demonstrate that GenEDA significantly boosts advanced LLMs' (e.g., GPT-4o and DeepSeek-V3) performance in all tasks.