The widespread deployment of Large Language Models (LLMs) in software engineering has established a dominant paradigm: natural-language-to-code generation. While this prompt-to-code approach accelerates localized algorithmic composition and boilerplate construction, it creates significant systemic vulnerabilities when applied to complex, multi-tiered architectures. By generating source code directly from ambiguous natural language prompts, state-of-the-art AI systems bypass foundational structural design phases, resulting in architectural drift, hidden state space explosion, untracked cross-module coupling, and unverifiable invariants. This paper introduces the Model-Augmented Generation (MAG) framework, a formal methodology that re-establishes machine-verifiable software models as the mandatory intermediate layer between high-level human intent and executable source code. Rather than prompting neural models to emit unstructured target syntax, MAG prompts LLMs to synthesize formal, verifiable intermediate representations (IR) grounded in domain constraints, state machine semantics, and algebraic type systems. These models are statically verified using formal solvers before being compiled deterministically into production code. We evaluate MAG across an enterprise benchmark of 120 distributed software specifications against state-of-the-art token-centric generation baselines (Direct Prompting, Chain-of-Thought, and ReAct-driven Autonomous Agents). Our findings demonstrate that MAG reduces architectural divergence by 78.4%, eliminates 94.2% of invalid cross-domain state transitions, and reduces latent systemic bugs from 34.2% to 2.1%, while maintaining comparable development velocity. This research demonstrates that software models are not obsolete relics of pre-AI methodologies, but are the missing structural invariant required for robust, reliable, and mathematically verifiable AI-driven software engineering.