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Results Summary:
Results Summary:
We have included several additional baselines for both the synthetic energy experiments and conformer generation
New Synthetic Energy Baselines (DW4, LJ) (Section A):
Denoising Diffusion Sampler (DDS) [Vargas 2023],
Off-policy LogVariance [Richter 2023]
An ablation of Adjoint Sampling w/o Reciprocal Projection that only trains with sampled SDE trajectories and does not perform reciprocal projection.
New Metrics and Figures for (DW4, LJ) (Section A):
Effective sample size (ESS) and Evidence lower bounds (ELBO) [Zhang 2022, Blessing 2024].
Energy Histogram Plots
Run-time efficiency breakdown of Amortized Training (Section A).
New Amortized Molecular Conformer Baselines (SPICE, GEOM-DRUGS) (Section A):
iDEM [Akhound-Sadegh 2023] with 2 and 16 MC samples for estimating the loss.
Adjoint Sampling w/o Reciprocal Projection (ablation).
Molecular Data Details (Section B):
The distribution of molecular structures and some example conformers are described.
A. New Experimental Results
A. New Experimental Results
New Synthetic Energy Baselines and Metrics
New Synthetic Energy Baselines and Metrics
Table 1: Synthetic Energy Functions
New Conformer Generation Baselines
New Conformer Generation Baselines
Table 2: Amortized Conformer Generation
Energy Histograms
Energy Histograms
DW4
LJ13
Figure 1. Energy Histograms for Synthetic Energies.
LJ55
Run-time comparison on conformer generation where energy model is an invariant graph neural net
Run-time comparison on conformer generation where energy model is an invariant graph neural net
Runtime
Runtime
Shown as a percentage (%) of the SDE simulation.
Figure 2. Run-time Analysis Breakdown
B. Additional Dataset Information
B. Additional Dataset Information
Dataset distributions
Dataset distributions
Total Structures: >24,000,
Number of atoms statistics: mean: 37, Median: 39, Max: 50, Min: 3.
Num. of atoms histogram
Num. of atoms histogram
Figure 3. Molecule Dataset Size Histogram.
Example Molecules with 50 atoms (150 spatial dimension)
Example Molecules with 50 atoms (150 spatial dimension)
O=S(=O)(NCCc1c(-c2cc3ccccc3o2)[nH]c2ccccc12)c1ccc(Br)cc1
NC(=[NH2+])c1ccc2nc(C(=O)N(O)Cc3cccc(Oc4ccccc4)c3)[nH]c2c1
Figure 4. Example 50-atom Conformers
Cc1noc([C@@H]2Cc3ccc(NS(=O)(=O)O)cc3CN2C(=O)OC(C)(C)C)n1
C. Misc. Figures
C. Misc. Figures
Visualizing the Reciprocal Projection Trajectory Distribution vs Full Trajectory Sampling of Adjoint Sampling. Adjoint Matching
Visualizing the Reciprocal Projection Trajectory Distribution vs Full Trajectory Sampling of Adjoint Sampling. Adjoint Matching
Figure 5. Updates for AM and AS after consuming 256 Trajectories Respectively
Figure 6. Cartesian Atom Diffusion Visualization from Trained Adjoint Sampling Model.
Visualization of an unseen conformer structure generated by trained model.
Visualization of an unseen conformer structure generated by trained model.
References
References
[Vargas 2023] Denoising Diffusion Samplers
[Blessing 2024] Beyond ELBOs: A Large-Scale Evaluation of Variational Methods for Sampling
[Zhang 2022] Path Integral Sampler: a stochastic control approach for sampling
[Richter 2023] Improved sampling via learned diffusions
[Akhound-Sadegh 2023] Iterated Denoising Energy Matching for Sampling from Boltzmann Densities
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