In speaker verification, log-likelihood ratios (LLRs) from multiple systems can be fused to improve verification performance. Typically fusion applies a global transform to map a vector of system scores into a single output. However, information conveying input signal conditions can be leveraged, allowing system fusion to be condition-aware. This paper presents a framework for adaptive fusion, generalizing prior work from [1]. It proposes a generative model for multi-system speaker verification trials, which are drawn from a discrete set of underlying signal conditions. An Expectation-Maximization (EM) Algorithm is presented, which discovers relevant conditions in an unsupervised manner. Generative Condition-Aware (GCA) Fusion is then derived as the LLR of a vector of scores given the associated speaker embeddings. Experimental results show the proposed approach to provide performance improvements on multiple speaker verification tasks, relative to using logistic regression.