The training support is much less mature and much less widely used, but it does exit:
https://onnxruntime.ai/docs/get-started/training-on-device.h...
https://onnxruntime.ai/docs/get-started/training-pytorch.htm...
Eventually we went with pytorch only support for the time being, with still exploring OpenXLA in place of ONNX, as a universal adapter: https://github.com/ipcamit/colabfit-model-driver