Research map / Probabilistic and scientific modeling / Variational and generative sampling
Generator Matching: Generative modeling with arbitrary Markov processes
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Introduces Generator Matching, a framework that trains Markov generative models (flows, diffusions, jump processes, CTMCs) by regressing conditional generators with Bregman-divergence losses, and shows jump+flow Markov superposition improves image FID and protein generation diversity.
Problem
Generative modeling is usually restricted to specific Markov process classes (flows, diffusions, discrete diffusion) on specific state spaces; a unified, modality-agnostic framework is needed to characterize and train the full design space of Markov generative models.
Approach
Characterize generative models via generators of Markov processes; construct conditional generators that solve the Kolmogorov Forward Equation for single data points and train a neural generator on the marginal via a conditional Bregman-divergence loss; this unifies diffusion, flow, and discrete diffusion, and enables jump models, learned diffusion coefficients, and Markov superpositions.
Key results
- On CIFAR10, Jump + Flow Markov superposition with mixed sampling reaches FID 2.36, improving on the flow model with 2nd-order sampler (2.48).
- On ImageNet32, Jump + Flow superposition achieves FID 3.33 (mixed sampler) versus 3.59 for the flow model with 2nd-order sampler.
- Adding SO(3) jumps to pretrained MultiFlow without fine-tuning raises unimodal diversity from 0.52 to 0.63 while keeping novelty at 0.41.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add a jump model to the flow model using Markov superposition with Euler sampling | Flow model · CIFAR10 | FID: 2.94 -> 2.49 | Helped |
| Add a jump model to the flow model using Markov superposition with Euler sampling | Flow model · ImageNet32 | FID: 4.58 -> 3.47 | Helped |
| Use a jump model instead of a flow model with Euler sampling | Image generation · CIFAR10 | FID: 2.94 -> 4.23 | Hurt |
| Use a jump model instead of a flow model with Euler sampling | Image generation · ImageNet32 | FID: 4.58 -> 7.66 | Hurt |
| Use a Markov superposition with a 2nd order flow sampler and Euler jump sampler | Flow model (2nd order) · CIFAR10 | FID: 2.48 -> 2.36 | Helped |
| Use a Markov superposition with a 2nd order flow sampler and Euler jump sampler | Flow model (2nd order) · ImageNet32 | FID: 3.59 -> 3.33 | Helped |
| Add SO(3) jumps to MultiFlow | MultiFlow · Protein generation multimodal | Diversity: 0.38 -> 0.48 | Helped |
| Add SO(3) jumps to MultiFlow | MultiFlow · Protein generation multimodal | Novelty: 0.39 -> 0.41 | Helped |
| Add SO(3) jumps to MultiFlow | MultiFlow · Protein generation unimodal | Diversity: 0.52 -> 0.63 | Helped |
| Add SO(3) jumps to MultiFlow | MultiFlow · Protein generation unimodal | Novelty: 0.39 -> 0.41 | Helped |
| Add flow to the SO(3) jump model | MultiFlow with SO(3) jumps · Protein generation multimodal | Diversity: 0.48 -> 0.47 | Hurt |
| Add flow to the SO(3) jump model | MultiFlow with SO(3) jumps · Protein generation unimodal | Diversity: 0.63 -> 0.59 | Hurt |
Surprising findings
- A jump model alone is weaker than flows (CIFAR10 FID 4.23 vs 2.94 with Euler sampling), yet superposing it with a flow model improves over the flow alone.
Limitations
- Jump models lack classifier-free guidance and were evaluated only unconditionally.
- Jump models on R^d are sampled only with Euler sampling so far, limiting comparisons with higher-order flow samplers.
- Current jump model results lag behind state-of-the-art diffusion/flow models.
Experimental setup
Datasets: CIFAR10 ImageNet32
Benchmarks: CIFAR10 ImageNet32 protein generation benchmark (designability, diversity, novelty)
Metrics: FID designability diversity novelty
Baselines: DDPM VP-SDE EDM Flow model (Euler) RFdiffusion FrameFlow FoldFlow MultiFlow Protpardelle ProteinGenerator
Builds on: flow matching denoising diffusion models stochastic interpolants MultiFlow probability flow ODE
Closest papers by meaning
- Energy-based generator matching: A neural sampler for general state space (NeurIPS 2025 · similarity 0.90)
- Transition Matching: Scalable and Flexible Generative Modeling (NeurIPS 2025 · similarity 0.90)
- Flow Matching with General Discrete Paths: A Kinetic-Optimal Perspective (ICLR 2025 · similarity 0.87)
- Energy Matching: Unifying Flow Matching and Energy-Based Models for Generative Modeling (NeurIPS 2025 · similarity 0.87)
- Towards Non-Asymptotic Convergence for Diffusion-Based Generative Models (ICLR 2024 · similarity 0.87)
- Glauber Generative Model: Discrete Diffusion Models via Binary Classification (ICLR 2025 · similarity 0.86)
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