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Score distillation has emerged as one of the most prevalent approaches fortext-to-3D asset synthesis. Essentially, score distillation updates 3Dparameters by lifting and back-propagating scores averaged over differentviews. In this paper, we reveal that the gradient estimation in scoredistillation is inherent to high variance. Through the lens of variancereduction, the effectiveness of SDS and VSD can be interpreted as applicationsof various control variates to the Monte Carlo estimator of the distilledscore. Motivated by this rethinking and based on Stein's identity, we propose amore general solution to reduce variance for score distillation, termed SteinScore Distillation (SSD). SSD incorporates control variates constructed byStein identity, allowing for arbitrary baseline functions. This enables us toinclude flexible guidance priors and network architectures to explicitlyoptimize for variance reduction. In our experiments, the overall pipeline,dubbed SteinDreamer, is implemented by instantiating the control variate with amonocular depth estimator. The results suggest that SSD can effectively reducethe distillation variance and consistently improve visual quality for bothobject- and scene-level generation. Moreover, we demonstrate that SteinDreamerachieves faster convergence than existing methods due to more stable gradientupdates.

SteinDreamer: Variance Reduction for Text-to-3D Score Distillation via Stein Identity