Optimizing the Transport Problem for Conditional, Flow-Based Generation

Flow-based generative models have made significant progress in AI research in recent years. They enable the generation of complex data, such as images or text, by transforming a simple distribution, e.g., a Gaussian distribution, into a complex target data distribution. A crucial component of these models is the so-called "flow," which performs the transformation step by step. Optimizing this flow is critical for the quality of the generated data.

One method for optimizing the flow is the Optimal Transport (OT) problem. Simply put, OT searches for the most efficient way to transport mass from one distribution to another. In the context of flow-based models, OT is used to control the transformation process and maximize the similarity between the generated distribution and the target data distribution. In practice, a simplified variant, called Minibatch Optimal Transport, is often used to reduce the computational cost.

However, recent research findings show that Minibatch Optimal Transport reaches its limits in the context of conditional flow-based generation. Conditional generation means that the generated data depends on an additional input, the condition. For example, the condition could be a text description that specifies the image to be generated. The problem is that conventional Minibatch Optimal Transport ignores the conditions when calculating the optimal transport. This leads to a biased prior distribution during training, which does not match the unbiased prior distribution used to generate data.

This discrepancy between training and generation leads to suboptimal results. To solve this problem, a new approach called Conditional Optimal Transport (C²OT) has been developed. C²OT extends the classic Optimal Transport problem by adding a condition-dependent weighting factor to the cost matrix. This factor takes the conditions into account when calculating the optimal transport, thus allowing for a better adaptation to the target data distribution.

Experimental results show that C²OT can be successfully used with both discrete and continuous conditions. The method was evaluated using various datasets, including CIFAR-10, ImageNet-32x32, and ImageNet-256x256, and showed improved performance compared to existing methods. The improvement was evident across various budgets for function evaluations, suggesting the robustness of the approach.

The development of C²OT represents a significant advancement in the field of conditional, flow-based generation. By considering the conditions during the optimization of the transport, more realistic and higher-quality data can be generated. These advancements are particularly relevant for applications such as image synthesis, text generation, and other areas where the generation of data under specific conditions plays an important role.

For Mindverse, a German company specializing in AI-powered content creation, these developments are of particular interest. The improved generation of content under specific conditions opens up new possibilities for the automated creation of texts, images, and other media. Integrating C²OT into the Mindverse platform could further enhance the quality and efficiency of content creation and offer users new creative opportunities.

Bibliographie: - Cheng, H. K., & Schwing, A. (2025). The Curse of Conditions: Analyzing and Improving Optimal Transport for Conditional Flow-Based Generation. arXiv preprint arXiv:2503.10636. - https://huggingface.co/papers/2503.10636 - https://huggingface.co/papers - https://www.sciencedirect.com/science/article/abs/pii/S0021999123002504 - https://en.wikipedia.org/wiki/Monte_Carlo_method