Do generative model produce varying outputs for same input
This depends entirely on the specific model. There are generative models, like most Generative Adversarial Networks (GANs) that receive a random number and generate data. There are other generative models that generate a probability distribution over the output space (e.g. text generation models), and therefore whether the model generates data deterministically depends on the inference procedure (e.g. greedy, sampling, beam search).
If you want your model to generate outputs deterministically, you just select a model and inference method that assures that.
In your example, you may have a normal seq2seq model (e.g. Transformer) and use beam search for decoding, and the outputs will be the same given the same input.