Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

GLASS Flows: Transition Sampling for Alignment of Flow and Diffusion Models

Peter Holderrieth, Uriel Singer, Tommi Jaakkola, Ricky T. Q. Chen, Yaron Lipman, Brian Karrer

TL;DR

GLASS Flows address the inefficiency of reward-alignment methods that rely on stochastic sampling by enabling efficient ODE-based sampling of Markov transitions $p_{t'|t}$ via an inner, retrievable flow-matching model derived through sufficient statistics. This unifies the efficiency of ODE sampling with the stochasticity of SDEs, improving text-to-image generation performance when combined with reward-alignment techniques like Feynman-Kac Steering and reward guidance. The approach yields a theoretical framework for constructing transitions, practical algorithms for posterior sampling and SMC, and strong empirical gains on large-scale models, effectively removing the efficiency-stochasticity tradeoff in inference-time scaling. Overall, GLASS Flows serve as a plug-in, training-free enhancement for reward-aligned sampling across flow and diffusion models with clear practical impact for scalable, high-quality generation.

Abstract

The performance of flow matching and diffusion models can be greatly improved at inference time using reward alignment algorithms, yet efficiency remains a major limitation. While several algorithms were proposed, we demonstrate that a common bottleneck is the sampling method these algorithms rely on: many algorithms require to sample Markov transitions via SDE sampling, which is significantly less efficient and often less performant than ODE sampling. To remove this bottleneck, we introduce GLASS Flows, a new sampling paradigm that simulates a "flow matching model within a flow matching model" to sample Markov transitions. As we show in this work, this "inner" flow matching model can be retrieved from a pre-trained model without any re-training, combining the efficiency of ODEs with the stochastic evolution of SDEs. On large-scale text-to-image models, we show that GLASS Flows eliminate the trade-off between stochastic evolution and efficiency. Combined with Feynman-Kac Steering, GLASS Flows improve state-of-the-art performance in text-to-image generation, making it a simple, drop-in solution for inference-time scaling of flow and diffusion models.

GLASS Flows: Transition Sampling for Alignment of Flow and Diffusion Models

TL;DR

GLASS Flows address the inefficiency of reward-alignment methods that rely on stochastic sampling by enabling efficient ODE-based sampling of Markov transitions via an inner, retrievable flow-matching model derived through sufficient statistics. This unifies the efficiency of ODE sampling with the stochasticity of SDEs, improving text-to-image generation performance when combined with reward-alignment techniques like Feynman-Kac Steering and reward guidance. The approach yields a theoretical framework for constructing transitions, practical algorithms for posterior sampling and SMC, and strong empirical gains on large-scale models, effectively removing the efficiency-stochasticity tradeoff in inference-time scaling. Overall, GLASS Flows serve as a plug-in, training-free enhancement for reward-aligned sampling across flow and diffusion models with clear practical impact for scalable, high-quality generation.

Abstract

The performance of flow matching and diffusion models can be greatly improved at inference time using reward alignment algorithms, yet efficiency remains a major limitation. While several algorithms were proposed, we demonstrate that a common bottleneck is the sampling method these algorithms rely on: many algorithms require to sample Markov transitions via SDE sampling, which is significantly less efficient and often less performant than ODE sampling. To remove this bottleneck, we introduce GLASS Flows, a new sampling paradigm that simulates a "flow matching model within a flow matching model" to sample Markov transitions. As we show in this work, this "inner" flow matching model can be retrieved from a pre-trained model without any re-training, combining the efficiency of ODEs with the stochastic evolution of SDEs. On large-scale text-to-image models, we show that GLASS Flows eliminate the trade-off between stochastic evolution and efficiency. Combined with Feynman-Kac Steering, GLASS Flows improve state-of-the-art performance in text-to-image generation, making it a simple, drop-in solution for inference-time scaling of flow and diffusion models.

Paper Structure

This paper contains 44 sections, 7 theorems, 101 equations, 14 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background and Motivation
  3. Motivation: Efficient Transitions for Reward Alignment
  4. GLASS Flows
  5. GLASS Transitions
  6. Constructing the velocity field
  7. GLASS denoiser
  8. GLASS velocity field
  9. Inference-time reward alignment with GLASS
  10. Related Work
  11. Experiments
  12. Efficient Posterior Sampling and Value Function Estimation
  13. Novel Sampling Methods
  14. Sequential Monte Carlo experiments
  15. Conclusion
  16. ...and 29 more sections

Key Result

Proposition 0

For $\rho=\frac{\alpha_t\sigma_{t'}}{\sigma_{t}\alpha_{t'}}$, we get that: $p_{t'|t}^{\text{DDPM}}(X_{t'}|X_{t})=p_{t'|t}(X_{t'}|X_{t})$, i.e. DDPM transitions are a special case of GLASS transitions.

Figures (14)

  • Figure 1: GLASS Flows overview. Left: Sampling transition $p_{t'|t}(x_{t'}|x_t)$ with GLASS Flows. Initial Gaussian samples $\bar{x}_{s=0}$ are evolved from inner time $s=0$ to $s=1$ via the velocity field $u_s(\bar{x}_s|x_t,t)$ that is obtained by transforming a pre-trained flow matching model. Right: Reward alignment with GLASS Flows improves text-image alignment.
  • Figure 2: Posterior sampling experiments. We noise images and then sample from the posterior $z\sim p_{1|t}(\cdot|x)$ via DDPM or GLASS Flows. Left: Examples for $t=0.2$ and $M=6$ simulation steps. Middle: FID values for various simulation steps $M$ and time $t$. Right: Estimation of the value function as assessed by correlation with ground truth (200 Monte Carlo samples with $M=200$).
  • Figure 3: Sampling from SiT/FLUX with various sampling methods. Left: Comparison with FLUX of images generated with DDPM vs. GLASS Flows. DDPM samples are more blurry and of lower quality. Middle: Results for SiT. Right: Results for FLUX. Prompts: "Carrots" and "Refrigerator".
  • Figure 4: Detailed results for \ref{['fig:posterior_flows_summary_figure']} (Middle). Comparing the performance of sampling the posterior $p_{1|t}$ via GLASS Flows (Ours) and SDE (DDPM) sampling. Ablate over different times $t$ and sampling steps. GLASS Flows achieve significantly lower FID for lower number of sampling steps than DDPM sampling.
  • Figure 5: Detailed results for \ref{['fig:posterior_flows_summary_figure']} (Right). Comparing the performance of estimating the value function $V_t(x)$ via sampling the posterior $p_{1|t}$ via GLASS Flows (Ours) and SDE (DDPM) sampling via correlation. Experiment performed for different times $t$ and sampling steps $M$. GLASS Flows achieve significantly higher correlation for lower number of steps than DDPM sampling. Ground truth is measured via 200 samples with 200 simulation steps of ODE/SDE.
  • ...and 9 more figures

Theorems & Definitions (11)

  • Proposition 0
  • Proposition 0
  • Theorem 0
  • Proposition 0
  • proof
  • Lemma 1: Equivalent observations for multivariate Gaussian
  • proof
  • Proposition 0
  • proof
  • Theorem 0
  • ...and 1 more