Scientific foundation models increasingly operate on continuous phenomena, yet still use discrete residual computation. We ask whether pretrained residual transformations can support additional latent computation without expanding the backbone. To test this possibility, we introduce Continuum-LM, which reuses these transformations as dynamical operators in a continuous-depth language model. Its hidden states evolve through an ordinary differential equation evaluated by higher-order numerical integration, with solver order and step size controlling computation. Across eight scientific tasks, Continuum-LM trains stably and improves mean exact-match accuracy by 7.77 and 10.96 percentage points over discrete counterparts at the 0.6B and 1.7B scales, respectively. At 0.6B, it also outperforms an Ouro-style recurrent control under matched parameter and residual-function evaluation budgets. Together, these results support extensible computational depth through parameter reuse, identifying continuous hidden-state evolution as a practical design dimension for scientific language models beyond parameter scaling.

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