SteinDreamer: Variance Reduction for Text-to-3D Score Distillation via
  Stein Identity
Authors: name: Peihao Wang, name: Zhiwen Fan, name: Dejia Xu, name: Dilin Wang, name: Sreyas Mohan, name: Forrest Iandola, name: Rakesh Ranjan, name: Yilei Li, name: Qiang Liu, name: Zhangyang Wang, name: Vikas Chandra

Score distillation has emerged as one of the most prevalent approaches for
text-to-3D asset synthesis. Essentially, score distillation updates 3D
parameters by lifting and back-propagating scores averaged over different
views. In this paper, we reveal that the gradient estimation in score
distillation is inherent to high variance. Through the lens of variance
reduction, the effectiveness of SDS and VSD can be interpreted as applications
of various control variates to the Monte Carlo estimator of the distilled
score. Motivated by this rethinking and based on Stein's identity, we propose a
more general solution to reduce variance for score distillation, termed Stein
Score Distillation (SSD). SSD incorporates control variates constructed by
Stein identity, allowing for arbitrary baseline functions. This enables us to
include flexible guidance priors and network architectures to explicitly
optimize for variance reduction. In our experiments, the overall pipeline,
dubbed SteinDreamer, is implemented by instantiating the control variate with a
monocular depth estimator. The results suggest that SSD can effectively reduce
the distillation variance and consistently improve visual quality for both
object- and scene-level generation. Moreover, we demonstrate that SteinDreamer
achieves faster convergence than existing methods due to more stable gradient
updates.