# Training-Free Guidance Beyond Differentiability: Scalable Path Steering with Tree Search in Diffusion and Flow Models

arXiv: https://arxiv.org/abs/2502.11420 · HTML: https://mlsanity.com/paper/2502.11420/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 65 of its 87 references that are in the map.
- First posted on arXiv 17 Feb 2025.

## Builds on (most cited first, 30 of 65)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Diffusion Model Alignment Using Direct Preference Optimization](https://mlsanity.com/paper/2311.12908/) (2023)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [FreeDoM: Training-Free Energy-Guided Conditional Diffusion Model](https://mlsanity.com/paper/2303.09833/) (2023)
- [Aligning Text-to-Image Diffusion Models with Reward Backpropagation](https://mlsanity.com/paper/2310.03739/) (2023)
- [Therapeutics Data Commons: Machine Learning Datasets and Tasks for Drug Discovery and Development](https://mlsanity.com/paper/2102.09548/) (2021)
- [Inference-Time Scaling for Diffusion Models beyond Scaling Denoising Steps](https://mlsanity.com/paper/2501.09732/) (2025)
- [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [A General Framework for Inference-time Scaling and Steering of Diffusion Models](https://mlsanity.com/paper/2501.06848/) (2025)
- [Enabling Factorized Piano Music Modeling and Generation with the MAESTRO Dataset](https://mlsanity.com/paper/1810.12247/) (2018)

## Built on by (most cited first, 24 of 24)

- [Inference-time Scaling of Diffusion Models through Classical Search](https://mlsanity.com/paper/2505.23614/) (2025)
- [Dynamic Search for Inference-Time Alignment in Diffusion Models](https://mlsanity.com/paper/2503.02039/) (2025)
- [Feedback Guidance of Diffusion Models](https://mlsanity.com/paper/2506.06085/) (2025)
- [HardFlow: Hard-Constrained Sampling for Flow-Matching Models via Trajectory Optimization](https://mlsanity.com/paper/2511.08425/) (2025)
- [Training-Free Adaptation of Diffusion Models via Doob's h-Transform](https://mlsanity.com/paper/2602.16198/) (2026)
- [Inference-Time Scaling of Diffusion Language Models via Trajectory Refinement](https://mlsanity.com/paper/2507.08390/) (2025)
- [AutoRefiner: Improving Autoregressive Video Diffusion Models via Reflective Refinement Over the Stochastic Sampling Path](https://mlsanity.com/paper/2512.11203/) (2025)
- [Entropy Aware Reward Guidance for Diffusion Language Model Alignment](https://mlsanity.com/paper/2602.05000/) (2026)
- [Tree Reward-Aligned Search for TReASURe in Masked Diffusion Language Models](https://mlsanity.com/paper/2509.23146/) (2025)
- [Local MAP Sampling for Diffusion Models](https://mlsanity.com/paper/2510.07343/) (2025)
- [Inference-Time Scaling in Diffusion Models through Iterative Partial Refinement](https://mlsanity.com/paper/2605.19317/) (2026)
- [Search-Augmented Masked Diffusion Models for Constrained Generation](https://mlsanity.com/paper/2602.02727/) (2026)
- [Slowly Annealed Langevin Dynamics: Theory and Applications to Training-Free Guided Generation](https://mlsanity.com/paper/2605.07950/) (2026)
- [BFMT: Enhancing Search Capabilities of Tree Sampler via Bootstrap Flow-Map Tree](https://mlsanity.com/paper/2607.02915/) (2026)
- [VGAS: Variance-Reduced Guidance and Adaptive Selection for Training-Free Reward Alignment in Discrete Diffusion](https://mlsanity.com/paper/2608.26585/) (2026)
- [Guiding Diffusion with Deep Geometric Moments: Balancing Fidelity and Variation](https://mlsanity.com/paper/2505.12486/) (2025)
- [Iterative Inference-time Scaling with Adaptive Frequency Steering for Image Super-Resolution](https://mlsanity.com/paper/2512.23532/) (2025)
- [Flow-Direct: Feedback-Efficient and Reusable Guidance for Flow Models via Non-Parametric Guidance Field](https://mlsanity.com/paper/2605.16348/) (2026)
- [Histogram-constrained Image Generation](https://mlsanity.com/paper/2606.31683/) (2026)
- [Feature-Space Guided Diffusion for Realistic Ultrasound Image Synthesis](https://mlsanity.com/paper/2607.11655/) (2026)
- [LC-GRPO: Bridging Train-Inference Gap for Flow-Based GRPO with Langevin Correction](https://mlsanity.com/paper/2608.05600/) (2026)
- [Language-Informed Flow Matching for Trend-Guided Structure-Based 3D Molecular Generation](https://mlsanity.com/paper/2608.31009/) (2026)
- [LATS: Levy Adaptive Tree Sampling for Feedback-Driven Diverse Target Discovery](https://mlsanity.com/paper/2609.06761/) (2026)
- [RIDE: Reference-Anchored Inference-Time Diffusion Editing for Scaffold Hopping](https://mlsanity.com/paper/2609.35623/) (2026)

## Abstract (arXiv)

Training-free guidance enables controlled generation in diffusion and flow models, but most methods rely on gradients and assume differentiable objectives. This work focuses on training-free guidance addressing challenges from non-differentiable objectives and discrete data distributions. We propose TreeG: Tree Search-Based Path Steering Guidance, applicable to both continuous and discrete settings in diffusion and flow models. TreeG offers a unified framework for training-free guidance by proposing, evaluating, and selecting candidates at each step, enhanced with tree search over active paths and parallel exploration. We comprehensively investigate the design space of TreeG over the candidate proposal module and the evaluation function, instantiating TreeG into three novel algorithms. Our experiments show that TreeG consistently outperforms top guidance baselines in symbolic music generation, small molecule design, and enhancer DNA design with improvements of 29.01%, 16.6%, and 18.43%. Additionally, we identify an inference-time scaling law showing TreeG's scalability in inference-time computation.