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Advancing LLM reasoning skills has captivated wide interest. However, current post-training techniques rely heavily on supervisory signals, such as outcome supervision or auxiliary reward models, which face the problem of scalability and high annotation costs. This motivates us to enhance LLM reasoning without the need for external supervision. Given the input query, the LLM seeks the globally optimal response by stepwise sampling and self-rewarding, and optimizes itself with the collected responses. Genius offers some technical solutions to address the following key challenges. To tackle the problem of how to determine the steps in the response via self-rewarding, Genius introduces a stepwise foresight re-sampling strategy to sample and estimate the step value by simulating future outcomes. Recognizing the intrinsic noise and uncertainty of self-supervision, we propose an advantage-calibrated optimization (ACO) loss function to mitigate estimation inconsistencies. In short, Genius provides an advanced initial step towards self-improve LLM reasoning with general queries and without supervision, revolutionizing reasoning scaling laws given the vast availability of general queries.