Bayesian optimization (BO) over discrete spaces is challenging due to missing gradients and the sparsity of valid solutions.
Latent-space BO sidesteps both issues by fitting a surrogate in the latent space of a generative model, which however substantially complicates the direct incorporation of domain knowledge that is naturally expressed in the original discrete space.
In this work, we instead combine a pretrained generative model with a surrogate defined directly in data space, where inductive biases such as domain-specific kernels can be readily incorporated.
Rather than maximizing the acquisition function over the discrete design space, our method samples candidates from the generative model under a distribution tilted by the acquisition function.
To recover useful gradients for sampling, we embed this tilted distribution into a diffusion bridge that yields a smooth, posterior-averaged acquisition function.
This leads to acquisition function guided generation (AFGG), which we instantiate with a categorical diffusion model and an autoregressive normalizing flow.
Across a broad suite of molecular benchmarks, the diffusion model variant performs on par with leading BO methods, while the flow model variant outperforms state-of-the-art methods in most cases and remains highly competitive otherwise.
Our implementation is available at https://anonymous.4open.science/r/afgg.