We tackle the problem of text-driven 3D generation from a geometry alignment perspective. Given a set of the text prompts, we aim at the generation of a collection of objects with their semantically corresponding parts being aligned between these objects. Recent methods based on Score Distillation have succeeded in distilling the knowledge from 2D diffusion models to high-quality representations of the 3D objects. These methods handle multiple text queries separately, and therefore the resulting objects have a high variability in object pose and structure. However, in some applications, such as 3D asset design, it may be desirable to obtain a set of objects aligned with each other. In order to achieve the alignment of the corresponding parts of the generated objects, we propose to embed these objects into a common latent space and optimize the continuous transitions between these objects. We enforce two kinds of properties of these transitions: smoothness of the transition and plausibility of the intermediate objects along the transition. We demonstrate that both of this properties are essential for good alignment. We provide several practical scenarios that benefit from alignment between the objects, including 3D editing and object hybridization, and experimentally demonstrate the effectiveness of our method.