Conditioning Diffusions Using Malliavin Calculus
Authors: Jakiw Pidstrigach, Elizabeth Louise Baker, Carles Domingo-Enrich, George Deligiannidis, Nikolas Nüsken
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we do an empirical evaluation of our methods. Full experimental details are provided in Appendix C. In Section 4.1 and Section 4.2 we study the case of diffusion bridges, i.e. Y = XT , or a Dirac-delta reward function g, since this can be seen as the most challenging setup: In Section 4.1, we conduct experiments where the true transition densities are available for evaluation. In Section 4.2, we demonstrate our method on bridges of stochastic shape processes, which have applications in biology. We also compare to related methods (Heng et al., 2022) and (Baker et al., 2025) and show favourable results. |
| Researcher Affiliation | Collaboration | 1Department of Statistics, University of Oxford, UK 2Department of Computer Science, University of Copenhagen, Denmark 3Microsoft Research New England, Cambridge, USA 4Department of Mathematics, King s College, London, UK. |
| Pseudocode | Yes | Algorithm 1 BEL Training Step Algorithm 2 Adjoint SDE Method for Calculating Ss |
| Open Source Code | No | The paper does not provide an explicit statement or link for the open-sourcing of the code for the methodology described in this paper. |
| Open Datasets | Yes | We train a diffusion model using a flow matching loss with a U-Net architecture on the Fashion-MNIST dataset (Xiao et al., 2017). |
| Dataset Splits | No | The paper does not provide specific train/test/validation dataset splits for the experiments. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., exact GPU/CPU models, memory amounts) used for running its experiments. |
| Software Dependencies | No | The paper mentions using the Adam optimizer but does not specify versions for programming languages, libraries, or other key software components used in the implementation. |
| Experiment Setup | Yes | We discretised the time domain [0, 1] into 200 equivariant grid points for the simulation... We used a batch size of 2048 and iterated through 20 000 batches. We used the Adam optimizer and a neural network architecture which is loosely inspired by UNets. It projects the input data up to 256 dimensions and then has fully connected layers of size [256, 128, 64, 32, 64, 128, 256] with skip connections. The last layer is then a fully connected layer to the output dimension. For the algorithms BEL first and BEL last we used δt = 1/200. For the kernel parameters in the SDE (32) we set κ = 0.1 and β = 1.0. For each method, we train on a total of 102.400 trajectories with a batch size of 128. |