Rethinking Losses for Diffusion Bridge Samplers (2506.10982v1)

Abstract: Diffusion bridges are a promising class of deep-learning methods for sampling from unnormalized distributions. Recent works show that the Log Variance (LV) loss consistently outperforms the reverse Kullback-Leibler (rKL) loss when using the reparametrization trick to compute rKL-gradients. While the on-policy LV loss yields identical gradients to the rKL loss when combined with the log-derivative trick for diffusion samplers with non-learnable forward processes, this equivalence does not hold for diffusion bridges or when diffusion coefficients are learned. Based on this insight we argue that for diffusion bridges the LV loss does not represent an optimization objective that can be motivated like the rKL loss via the data processing inequality. Our analysis shows that employing the rKL loss with the log-derivative trick (rKL-LD) does not only avoid these conceptual problems but also consistently outperforms the LV loss. Experimental results with different types of diffusion bridges on challenging benchmarks show that samplers trained with the rKL-LD loss achieve better performance. From a practical perspective we find that rKL-LD requires significantly less hyperparameter optimization and yields more stable training behavior.

• The paper challenges the conventional log variance loss by exposing its theoretical shortcomings in diffusion bridge sampling.
• The paper advocates for rKL loss combined with the log-derivative trick (rKL-LD) to ensure stable training and reduced hyperparameter tuning.
• The paper introduces learnable diffusion coefficients to dynamically balance exploration and exploitation, improving overall sampling performance.

Expert Analysis of "Rethinking Losses for Diffusion Bridge Samplers"

The paper "Rethinking Losses for Diffusion Bridge Samplers" offers an in-depth exploration of loss functions in the field of diffusion bridge sampling—a methodology crucial for generating samples from unnormalized distributions, often encountered in fields such as computational physics, chemistry, and Bayesian inference. Authored by experts in AI and machine learning, the paper focuses on the comparative efficacy and theoretical underpinnings of loss functions applied in diffusion bridge samplers.

Core Contributions

The paper makes several key contributions to the understanding and optimization of diffusion bridge samplers:

1. Critique of the Log Variance Loss: The authors challenge the widespread use of the Log Variance (LV) loss in training diffusion bridge samplers. While previous work suggests LV loss surpasses the reverse Kullback-Leibler (rKL) loss when employing the reparameterization trick, this paper reveals scenarios where LV fails to maintain its advantages. Particularly, LV lacks theoretical motivation akin to that of rKL, as the data processing inequality does not hold for the LV approach when applied to diffusion bridges.
2. Advocacy for rKL Loss with Log-Derivative Trick: A significant emphasis is placed on re-evaluating the rKL loss when combined with the log-derivative trick (rKL-LD). This combination sidesteps the conceptual pitfalls associated with LV use and empirically demonstrates superior performance in training diffusion samplers. The rKL-LD approach not only ensures stable training behavior but also necessitates less hyperparameter tuning, offering a pragmatic advantage in model development.
3. Introduction of Learnable Diffusion Coefficients: The research advocates learning diffusion coefficients within the sampling process. This adaptive strategy dynamically balances exploration and exploitation characteristics, enhancing the versatility and performance of diffusion bridge samplers à la rKL-LD loss framework.

Experimental Insights

The paper reports comprehensive experimental results across various benchmarks, including Bayesian learning tasks and synthetic target sampling. These results underscore the practical benefits of the rKL-LD loss, especially when diffusion coefficients are also subjected to learning processes. On tasks such as training Bayesian models and sampling from Gaussian mixtures, rKL-LD demonstrably improved sampling accuracy and model robustness compared to LV and rKL losses with other gradient estimation techniques.

Theoretical Implications

From a theoretical standpoint, the mismatch between LV loss and diffusion bridges highlights the importance of aligning generative model training objectives with foundational principles such as the data processing inequality. Models that do not satisfy this inequality might introduce biases or training inefficiencies, particularly in complex sampling contexts.

Future Directions

The paper paves the way for advancing AI through smarter sampling strategies. Learning more expressive latent variables and better handling of unnormalized distributions remain promising avenues for future research. Furthermore, exploring how rKL-LD can be integrated with reinforcement learning or combinatorial optimization paradigms could yield novel AI applications.

Conclusion

In summary, "Rethinking Losses for Diffusion Bridge Samplers" is a significant contribution to the field of AI model training, particularly in refining sampling from complex distributions. Through a blend of theoretical critique and empirical validation, it challenges preconceived notions about existing loss functions and opens up new possibilities for enhancing the efficacy of diffusion-based sampling methods.