From Optimization to Generation: Learning Portfolio Distributions with Simplex-Space Flow Matching

Portfolio construction typically seeks a single optimal portfolio from a market state, while the uncertainty and diversity of feasible investment decisions remain largely unexplored. In this work, we formulate portfolio construction as a conditional generative modeling problem, where the objective is to learn a distribution over feasible portfolio allocations conditioned on the observed market state, rather than predicting a single deterministic portfolio. We introduce Simplex-Space Flow Matching (SS-FM), which learns continuous probability flows directly over the portfolio simplex and generates diverse allocations that reflect different portfolio preferences. SS-FM generates diverse feasible portfolio candidates, while reinforcement learning learns how to make decisions within this generated candidate space using realized portfolio-level feedback, enabling the model to move beyond imitation of predefined portfolio construction rules. To provide informative conditioning signals, we incorporate overnight market information into alpha prediction through gated residual fusion, capturing information that is not contained in intraday price and volume dynamics. Experiments on the CSI 500 and S&P 500 demonstrate that modeling portfolio construction as conditional generation provides an effective alternative to deterministic and conventional optimization-based approaches.