Reliable physics simulation demands two capabilities that today's neural PDE solvers do not deliver together: generalization across heterogeneous PDE families, and stability under long autoregressive rollouts. Deterministic operators accumulate error geometrically, while existing probabilistic solvers are confined to a single PDE family or short horizons. We close this gap with the \textbf{Latent Generative Solver} (LGS), three coupled components: (i) a Physics VAE (PhyVAE) compressing twelve PDE families into a shared latent manifold; (ii) a Pyramidal Flow-Forcing Transformer (PFlowFT) that generates the next latent by flow matching, conditioned on a per-trajectory context updated on the model's own predictions; and (iii) input noising during training, for which we derive a sufficient-condition contraction bound explaining the observed long-horizon stability. Pretrained on a 2.5\,M-trajectory, 16-system corpus at $128^2$, LGS matches the strongest deterministic baseline at one step, wins on 15/16 systems at both 5- and 10-step rollout, cuts 20-step L2RE from $56.1\%$ to $\mathbf{30.2\%}$, and uses $\mathbf{13}$--$\mathbf{77\times}$ less recurrent dynamics-step compute. It also adapts efficiently to a $256^2$ Kolmogorov flow held out from the pretraining corpus, dropping 1-step L2RE from $0.398$ to $0.129$ in five finetune epochs against U-AFNO's $0.653{\to}0.343$.