For multivariate co-generation in scientific applications, we advocate pairwise block rather than joint modeling of all variables. This design mitigates the computational burden and data imbalance. To this end, we propose an Annealed Co-Generation (ACG) framework that replaces high-dimensional diffusion modeling with a low-dimensional diffusion model, which enables multivariate co-generation by composing pairwise variable generations. We first train an unconditional diffusion model over causal variables that are disentangled into pairs. At inference time, we recover the joint distribution by coupling these pairwise models through shared common variables, enabling coherent multivariate generation without any additional training. By employing a three-stage annealing process-Consensus, Heating, and Cooling-our method enforces consistency across shared common variables and progressively constrains each pairwise data distribution to lie on a learnable manifold, while maintaining high likelihood within each pair. We demonstrate the framework's flexibility and efficacy on two distinct scientific tasks: flow-field completion and antibody generation. All datasets and code will be made publicly available upon publication.
Figures & tables
Figure 1: Naive consensus vs. annealed consensus . (a) Given two diffusion processes that generate variable pairs (A,B1) and (B2,C) , if we wish t B1 and B2 to be the same B in the end, we can enforce consensus at each step of the process. However, this can easily yield implausible (low-likelihood) pairwise samples. (b) To avoid this, ACG introduces a heating–cooling schedule that temporarily splits B into B1 and B2 , enabling the model to preserve strong within-pair dependencies while refining the solution through multiple re-generations that help it escape local minima before restoring agreement.
Figure 2: Initialization for Different Tasks. (a) Flow Field Inpainting: Based on the left-to-right flow, only adjacent regions are used for inpainting to maintain left–right consistency. (b) Co-Antibody Generation: Using a pretrained model that jointly generates antigens and antibodies, we can design an antibody satisfying two antigens without additional training.
Model
Setting
MSE ( ↓ )
PSNR ( ↑ )
SSIM ( ↑ )
UNet [ 30 ]
Case
7.3232
16.270
0.3884
Joint modeling with optimization
RePaint [ 24 ]
Case
0.1878
32.388
0.6599
Pairwise modeling with optimization
ACG [ 54 ]
Patch
0.1320
34.003
0.7555
ACG/w [ 3 ]
Patch
0.1300
34.277
0.7448
Table 1: Experimental results for flow-velocity field inpainting.
Table 4: Results on baselines under a more realistic design setting. Main results for multi-specific antibody co-design on the Split-B benchmark.
Figure 4: Geometric Repair Analysis. Joint optimization may temporarily distort local geometry. The diffusion process subsequently corrects these inconsistencies and resolves steric clashes, restoring structural validity on the pretrained manifold.
Appendix figures & tables4 assets
Supplementary material from the paper’s appendix.
Appendix
Symbol
Description
Core Variables (Main Text)
B
Subject: The entity being designed (e.g., antibody sequence or structure).
A,C
Example contexts (targets) used in the main text.
B(A),B(C)
Branch-specific predictions of the subject.
Feature Decomposition
b
Intrinsic features of the subject B (its identity or style).
Appendix
Table 5: Summary of Notation and Symbols used in our framework.
Configuration
RMSD (Å) ( ↓ )
design-ipTM ( ↑ )
Ag. A
Ag. C
Avg.
Ag. A
Ag. C
Avg.
Exploration Depth (Iterations K )
Jheat=2,K=1
3.80
3.81
3.80
0.19
0.19
0.19
Jheat=2,K=2
3.87
3.89
3.88
0.18
0.18
0.18
Jheat=2,K=3
3.89
3.87
3.88
0.19
0.19
0.19
Jheat=2,K=4
3.91
4.00
3.96
0.18
0.18
0.18
Appendix
Table 6: Full ablation results on Split-A Weighted Fusion (Mean aggregation). This table consolidates all thermodynamic schedule grid searches.
Configuration
RMSD (Å) ( ↓ )
design-ipTM ( ↑ )
Ag. A
Ag. C
Avg.
Ag. A
Ag. C
Avg.
Exploration Depth (Iterations K )
Jheat=2,K=1
4.55
4.47
4.51
0.20
0.20
0.20
Jheat=2,K=2
4.60
4.54
4.57
0.20
0.20
0.20
Jheat=2,K=3
4.53
4.58
4.56
0.19
0.19
0.19
Jheat=2,K=4
4.46
4.44
4.45
0.18
0.19
0.19
Appendix
Table 7: Full ablation results on Split-A using Joint Overlap Factorization (DiffCollage-style) aggregation. Note that DiffCollage consistently underperforms compared to Mean aggregation (Table 6 ) in this high-dimensional constraints setting.
Target Pair
Configuration
RMSD (Å) ( ↓ )
design-ipTM ( ↑ )
Ag. A
Ag. C
Avg.
Ag. A
Ag. C
Avg.
4jre/4jr9
Single-target
2.80
2.97
2.89
0.47
0.31
0.39
Greedy
3.24
3.21
3.23
0.35
0.36
0.36
Greedy/w
2.72
2.92
2.82
0.34
0.38
0.36
Consistent
3.30
3.32
3.31
0.39
0.41
0.40
Consistent /w
2.77
2.59
2.68
0.43
0.41
0.42
Appendix
Table 8: Detailed per-target performance breakdown on the high-fidelity Split-B benchmark. This table expands upon the aggregate results in Table 4 , providing granular metrics for each of the 10 distinct antigen pairs. We compare the Independent Oracle (Single-target) against various joint optimization configurations. ACG/w consistently achieves the best balance of structural precision (RMSD) and binding confidence (design-ipTM) across diverse target topologies. Best performance is bolded.