Aiming at the problem of separation between generative behavior and creative intention in AI art creation, an intentionality-aware Bayesian generative model (IBGM) is proposed, which represents intentionality as a three-layer potential structure of global creative intention (16 dimensions), local decision intention (64 dimensions) and execution noise (32 dimensions). The aggregation probability graph is constructed through three channels of conditional prior, modulation transfer and backtracking correction. Sparse prior, rank-4 low-rank constraint and noise upper bound are used to achieve hierarchical identification and complexity control. The inference end constructs and generates topologically isomorphic structured variational family, dual-stream amortized encoder and variational inference-sequence Monte Carlo adaptive switching mechanism. Combined with analytical control variables and low-rank block design with block length 16, the effective degrees of freedom of the model are reduced from 4,144 to 320, and the complexity of single sequence inference is reduced by about one order of magnitude compared with the full covariance scheme. On 24,000 paired trajectories (training/validation/held out = 16,000/4,000/4,000, average trajectory length 64 steps), the mean squared error of IBGM global intention was reduced by about 30% compared with the strongest baseline, the correlation coefficient was increased by about 19%, and the posterior calibration KS distance was reduced to 0.03. The displacement increment of the set reached 0.14 (baseline 0.05-0.09), and the contribution ratio of hierarchical decomposition and structured variation was the top two, and the alignment distance of behavioral statistics was 0.16. The results show that intentionality can be rigorously modeled as a Bayesian computational object that can be generated, inferred, and identified.