We introduce ORIGEN, the first zero-shot method for 3D orientation grounding in text-to-image generation across multiple objects and diverse categories. While previous work on spatial grounding in image generation has mainly focused on 2D positioning, it lacks control over 3D orientation. To address this, we propose a reward-guided sampling approach using a pretrained discriminative model for 3D orientation estimation and a one-step text-to-image generative flow model. While gradient-ascent-based optimization is a natural choice for reward-based guidance, it struggles to maintain image realism. Instead, we adopt a sampling-based approach using Langevin dynamics, which extends gradient ascent by simply injecting random noise—requiring just a single additional line of code. Additionally, we introduce adaptive time rescaling based on the reward function to accelerate convergence. Our experiments show that \textsc{Origen} outperforms both training-based and test-time guidance methods across quantitative metrics and user studies.

Abstract In batch production systems, multiple items can be processed in the same batch if they share sufficiently similar production parameters. We consider the batch consolidation problem of minimizing the number of batches of a finite set of items. This article focuses on the case in which only one or two items can be processed in a single batch. The problem is NP ‐hard and cannot be approximated within 1.0021 of the optimum under the premise, P≠NP. However, the problem admits a ${{3}\over{2}}$ ‐approximation. The idea is to decompose the demands of items so that a maximum matching in the graph on the vertices of the decomposed demands provides a well‐consolidated batch set. © 2010 Wiley Periodicals, Inc. NETWORKS, Vol. 58(1), 12–19 2011