Intrinsic Distribution Matching

One- and few-step text-to-image generation must preserve fine-grained prompt fidelity with limited opportunities for refinement. Distribution matching distillation (DMD) guides a generator using the score difference between generated and reference distributions. Following prior work, we estimate this difference with internal velocity branches, avoiding a separate fake-score network. We ask whether an explicit moment constraint improves this learned score supervision. A decomposition of the reverse-KL field into a Gaussian moment component and a non-Gaussian residual identifies statistics that can be constrained explicitly. We introduce **Intrinsic Distribution Matching (IDM)**, which retains the full DMD correction and matches feature means and per-coordinate standard deviations using the generator's exponential-moving-average (EMA) copy, requiring no external feature encoder. Experiments use full-parameter and low-rank adaptation (LoRA) tuning on Z-Image-Turbo 6B and Qwen-Image 20B. At two network evaluations, IDM reaches 94.25% and 90.20% on Chinese and English LongText-Bench, the highest scores among the compared methods at this budget. Controlled ablations show gains from the added moment loss, while generator EMA features perform competitively with an external DINOv2 encoder across the five reported metrics.