Analyzing and Stabilizing Classifier Score Distillation for Text-to-Image Synthesis

Distribution Matching Distillation (DMD) accelerates diffusion and flow-matching models by compressing their iterative sampling process into a few steps. Recent work shows that its gradient can be decomposed into a DM term and a CFG-augmentation (CA) term, with CA providing a particularly strong distillation signal in text-to-image generation. Yet why CA is effective, and what constraints are needed to stabilize it, remain underexplored. To analyze its effectiveness, we first conduct synthetic experiments illustrating that finer condition groupings yield more discriminative classifier-score directions. We then probe the corresponding score-space mechanism in text-to-image models through interpolation, where retaining more fine-condition score information prolongs the effective distillation phase. These findings further support repositioning classifier score as the central distillation signal, motivating a reconsideration of stabilization within the classifier score distillation (CSD) framework. Within this framing, we ask whether sustaining CA necessarily requires online estimation of the evolving student distribution. We compare distribution matching, including fake and student side tracking strategies, with transition anchoring, which instead constrains student transitions using frozen teacher dynamics without maintaining an online fake-score model. We further equip transition-anchoring variants with a final-step perceptual loss to alleviate CA-induced oversaturation and local-detail degradation. Our empirical results show that both families improve training stability. On FLUX.2, transition anchoring variants achieve competitive performance with a 2.7-4.0x training speedup over vanilla DM, while revealing trade-offs between preference-oriented quality and alignment with the teacher distribution.