Generative ML models are increasingly popular in networking for tasks such as telemetry imputation, prediction, and synthetic trace generation. Despite their capabilities, they suffer from two shortcomings: \emph{(i)} their output is often visibly violating well-known networking rules, which undermines their trustworthiness; and \emph{(ii)} they are difficult to control, frequently requiring retraining even for minor changes. To address these limitations and unlock the benefits of generative models for networking, we propose a new paradigm for integrating explicit network knowledge, in the form of first-order logic rules, into ML models used for networking tasks. Rules capture well-known relationships among observed signals, e.g., that increased latency precedes packet loss. While the idea is conceptually straightforward, its realization is challenging: networking knowledge is rarely formalized into rules, and naively injecting rules into ML models often hampers their effectiveness. This paper introduces NetNomos, a multi-stage framework that \emph{(i)} learns rules directly from data (e.g., measurements); \emph{(ii)} filters them to select semantically meaningful ones; and \emph{(iii)} enforces them through collaborative generation between an ML model and a Satisfiability Modulo Theories (SMT) solver. %We evaluate NetNomos both component-wise and end-to-end across four diverse network datasets. We show that NetNomos learns diverse, meaningful rules from four real-world datasets and is 1.6--6.5$\times$ more scalable than DuoAI, a state-of-the-art (SOTA) rule-learning method. By enforcing these rules on a generic GPT-2 model, NetNomos achieves performance on par with or even surpassing specialized SOTA systems such as Zoom2Net and NetShare across three networking tasks: telemetry imputation, traffic forecasting, and synthetic data generation.