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Tokamak experiments record diverse measurements, including waveforms, profiles, fields, and scalars, which are used to reconstruct the plasma, forecast its evolution, recover associated control signals, and estimate disruption risk. Most models are built separately for one task and a fixed set of inputs and outputs, and each relies on a prescribed subset of diagnostics rather than structuring the full multimodal observation set to extract global, cross-signal information about the discharge. These limitations motivate a reusable foundation model that adapts to each task's input-output schema and models heterogeneous target signals jointly, rather than retraining a separate model for every configuration. In this work, we extend the TokaMark benchmark with two groups of tasks for actuator action inversion and disruption prediction, yielding 20 MAST tasks in six groups with explicit schemas and evaluation protocols. Then, we introduce GenToka, a generative tokamak foundation model that jointly generates schema-selected targets through a shared conditional diffusion Transformer, with signal-specific codecs preserving native time series, profiles, fields, and scalars; foundation pretraining and task-specific adaptation transfer cross-signal structure across all six groups. Evaluation on MAST measurements shows that GenToka reduces macro-average normalized root mean squared error relative to TokaMind by 4.7% on Groups 1-4 and by 17.7% on Group 5, and improves macro-average window-level F1 on Group 6 by 8.4% at a common validation-selected threshold. GenToka provides a reusable, generative, and multimodal pathway for experimental tokamaks, linking plasma-state reconstruction, actuator inference, and disruption warning from shared measurements to support more integrated, data-driven fusion plasma prediction and control research.