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The Superposition of Diffusion Models Using the Itô Density Estimator
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Proposes SuperDiff, a framework that combines multiple pre-trained diffusion models at inference via superposition of vector fields, using a new Itô density estimator that adds no overhead beyond sampling.
Problem
Combining multiple pre-trained diffusion models at generation time (without retraining) in a theoretically sound and efficient way, which requires estimating sample densities along SDE trajectories whose divergence estimates are costly.
Approach
Superpose the vector fields of several diffusion models reweighted by their marginal densities along the trajectory (OR as a softmax mixture, AND via solving a linear system for equal density change), and estimate those densities on the fly with a new Itô density estimator that needs no divergence computation.
Key results
- On CIFAR-10 disjoint halves, SuperDiff (OR) with T=100 reaches ODE FID 4.11, beating the model trained on the full dataset (FID 6.00).
- On concept interpolation with SD v1-4, SuperDiff (AND) raises min TIFA from 32.48 (averaging) to 39.92 and min CLIP from 24.23 to 24.79.
- For protein generation, SuperDiff (OR, l=1) improves designability (<2Å scRMSD 0.976 vs 0.928 for Proteus) and novelty (<0.5 scTM 0.396 vs 0.360).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SuperDiff (OR) rather than random choice between the two partition models | CIFAR-10 image generation · CIFAR-10 | FID (ODE): 4.28 -> 4.41 | Helped |
| Increase OR temperature from the default to T=100 (ablation) | SuperDiff (OR) · CIFAR-10 | FID (ODE): 4.41 -> 4.11 | Helped |
| Use SuperDiff (AND) instead of averaging SD outputs | Stable Diffusion v1-4 concept interpolation · Two-concept prompts | Min. TIFA: 32.48 -> 39.92 | Helped |
| Use SuperDiff (AND) instead of averaging SD outputs | Stable Diffusion v1-4 concept interpolation · Two-concept prompts | Min. CLIP: 24.23 -> 24.79 | Helped |
| Set protein-generation bias ℓ=1 instead of ℓ=0 (ablation) | SuperDiff (OR) · Protein generation | Designability (< 2 Å scRMSD): 0.752 \pm 0.03 -> 0.976 \pm 0.01 | Helped |
| Use SuperDiff (AND) instead of SuperDiff (OR), both with ℓ=0 (ablation) | Protein generation · Protein generation | Novelty (< 0.3 scTM): 0.008 \pm 0.01 -> 0.040 \pm 0.01 | Helped |
| Use SuperDiff (AND) instead of averaging scores | LDMol molecule generation · GSK3β + QED | Top-10 P1*P2: 0.154_{\pm 0.012} -> 0.177_{\pm 0.024} | Helped |
| Use SuperDiff (AND) instead of averaging scores | LDMol molecule generation · GSK3β + JNK3 | Top-10 P1*P2: 0.073_{\pm 0.013} -> 0.080_{\pm 0.025} | Helped |
| Use SuperDiff (AND) instead of joint prompting | LDMol molecule generation · GSK3β + JNK3 | Top-10 min(P1,P2): 0.186_{\pm 0.045} -> 0.209_{\pm 0.035} | Helped |
Surprising findings
- Combining FrameDiff (much less designable) with Proteus still yields designability above Proteus alone for SuperDiff (OR, l=1).
- The SuperDiff (OR) mixture on CIFAR-10 disjoint halves outperforms the model trained on the union of both halves in FID.
Limitations
- Computational cost is bounded by the cost of running each individual model; combination cannot be done by cheap weight merging.
- Requires access to each model's score function, which API-served models may not expose.
- Density estimation for ODE setting on SD is about 5x slower than the SDE setting (1082s vs 209s per image).
Experimental setup
Datasets: CIFAR-10 protein structure training sets (Proteus, FrameDiff) ZINC/therapeutic oracles (TDC)
Benchmarks: CIFAR-10 FID/IS/FLD CLIP score/ImageReward/TIFA on concept pairs protein designability/novelty/diversity metrics Therapeutics Data Commons molecule oracles
Metrics: FID IS FLD CLIP score ImageReward TIFA scRMSD scTM Frac. beta Tanimoto diversity
Baselines: Joint prompting Average of scores FrameDiff Proteus model trained on A∪B
Builds on: Hutchinson's trace estimator probability flow ODE denoising score matching classifier-free guidance
Closest papers by meaning
- Learning Diffusion Models with Flexible Representation Guidance (NeurIPS 2025 · similarity 0.88)
- SymDiff: Equivariant Diffusion via Stochastic Symmetrisation (ICLR 2025 · similarity 0.87)
- Taming Diffusion Prior for Image Super-Resolution with Domain Shift SDEs (NeurIPS 2024 · similarity 0.87)
- Immiscible Diffusion: Accelerating Diffusion Training with Noise Assignment (NeurIPS 2024 · similarity 0.87)
- Tortoise and Hare Guidance: Accelerating Diffusion Model Inference with Multirate Integration (NeurIPS 2025 · similarity 0.87)
- Multilevel and Sequential Monte Carlo for Training-Free Diffusion Guidance (NeurIPS 2026 · similarity 0.87)
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