mlsanityData to 14 Oct 2026

Ctrl-Z Sampling: Scaling Diffusion Sampling with Controlled Random Zigzag Explorations

arXiv 2506.20294 ↗First posted 25 Jun 2025cs.CVcited by 1

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Diffusion models generate conditional samples by progressively denoising Gaussian noise, yet the denoising trajectory can stall at visually plausible but low-quality outcomes with conditional misalignment or structural artifacts. We interpret this behavior as local optima in a surrogate quality landscape: Once early denoising commits to a suboptimal global structure, later steps mainly sharpen details and seldom correct the underlying mistake. While existing inference-time approaches explore alternative diffusion states via re-noising with fixed strength or direction, they exhibit limited capacity to escape steep quality plateaus. We propose Controlled Random Zigzag Sampling (Ctrl-Z Sampling),a scalable sampling strategy that detects plateaus in quality landscape via a surrogate score, and allocates exploration only when a plateau is detected. Upon detection, Ctrl-Z Sampling rolls back to noisier states, samples a set of alternative continuations, and updates the trajectory when a candidate improves the score, otherwise escalating the exploration depth to escape the current plateau. The proposed method is model-agnostic and broadly compatible with existing diffusion frameworks. Experiments show that Ctrl-Z Sampling consistently improves generation quality over other inference-time scaling samplers across different NFE budgets, offering a scalable compute-quality trade-off. Code available at: https://github.com/ShunqiM/Ctrl-Z-Sampling.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 102 of its 112 references that are in the map. First posted on arXiv 25 Jun 2025.

Builds on

102 of 112 references.

Closest ancestors · 33

Same direction, newest first

  1. 2025Inference-time Scaling of Diffusion Models through Classical Search29 May
  2. 2025Test-Time Scaling of Diffusion Models via Noise Trajectory Search24 May
  3. 2025Dynamic Search for Inference-Time Alignment in Diffusion Models3 Mar
  4. 2025A General Framework for Inference-time Scaling and Steering of Diffusion Models12 Jan
  5. 2025Test-time Alignment of Diffusion Models without Reward Over-optimization10 Jan
  6. 2024LaVin-DiT: Large Vision Diffusion Transformer18 Nov
  7. 2024Golden Noise for Diffusion Models: A Learning Framework14 Nov
  8. 2024Smoothed Energy Guidance: Guiding Diffusion Models with Reduced Energy Curvature of Attention1 Aug
  9. 2024CFG++: Manifold-constrained Classifier Free Guidance for Diffusion Models12 Jun
  10. 2024Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexity24 May
  11. 2024Learning to Discretize Denoising Diffusion ODEs24 May
  12. 2024Align Your Steps: Optimizing Sampling Schedules in Diffusion Models22 Apr
21 more
  1. 2023Faster Diffusion: Rethinking the Role of the Encoder for Diffusion Model Inference15 Dec
  2. 2023Exploiting the Signal-Leak Bias in Diffusion Models27 Sep
  3. 2023SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis4 Jul
  4. 2023Restart Sampling for Improving Generative Processes26 Jun
  5. 2023Parallel Sampling of Diffusion Models25 May
  6. 2023Structural Pruning for Diffusion Models18 May
  7. 2023Common Diffusion Noise Schedules and Sample Steps are Flawed15 May
  8. 2023Consistency Models2 Mar
  9. 2023Universal Guidance for Diffusion Models14 Feb
  10. 2023UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models9 Feb
  11. 2022Scalable Diffusion Models with Transformers19 Dec
  12. 2022DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models2 Nov
  13. 2022Classifier-Free Diffusion Guidance26 Jul
  14. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  15. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  16. 2022Fast Sampling of Diffusion Models with Exponential Integrator29 Apr
  17. 2022Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality11 Feb
  18. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  19. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  20. 2020Denoising Diffusion Implicit Models6 Oct
  21. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 69

  1. 2021Learning Transferable Visual Models From Natural Language Supervisioncited by 33,744
  2. 2020Language Models are Few-Shot Learnerscited by 32,419
  3. 2017Proximal Policy Optimization Algorithmscited by 15,215
  4. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  5. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  6. 2022ReAct: Synergizing Reasoning and Acting in Language Modelscited by 8,695
  7. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  8. 2020Scaling Laws for Neural Language Modelscited by 6,586
  9. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,355
  10. 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,708
  11. 2022Flow Matching for Generative Modelingcited by 5,702
  12. 2023Adding Conditional Control to Text-to-Image Diffusion Modelscited by 5,503
38 more
  1. 2022LAION-5B: An open large-scale dataset for training next generation image-text modelscited by 4,152
  2. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  3. 2023Let's Verify Step by Stepcited by 3,789
  4. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,700
  5. 2023Self-Refine: Iterative Refinement with Self-Feedbackcited by 3,442
  6. 2023Tree of Thoughts: Deliberate Problem Solving with Large Language Modelscited by 3,211
  7. 2022DreamFusion: Text-to-3D using 2D Diffusioncited by 3,025
  8. 2022Training Compute-Optimal Large Language Modelscited by 3,019
  9. 2023Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasetscited by 2,581
  10. 2021CLIPScore: A Reference-free Evaluation Metric for Image Captioningcited by 2,424
  11. 2022Video Diffusion Modelscited by 2,305
  12. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,354
  13. 2025s1: Simple test-time scalingcited by 1,341
  14. 2022Planning with Diffusion for Flexible Behavior Synthesiscited by 1,061
  15. 2022Diffusion-LM Improves Controllable Text Generationcited by 1,027
  16. 2024Large Language Monkeys: Scaling Inference Compute with Repeated Samplingcited by 991
  17. 2023Pick-a-Pic: An Open Dataset of User Preferences for Text-to-Image Generationcited by 977
  18. 2022STaR: Bootstrapping Reasoning With Reasoningcited by 940
  19. 2022Solving math word problems with process- and outcome-based feedbackcited by 901
  20. 2023Human Preference Score v2: A Solid Benchmark for Evaluating Human Preferences of Text-to-Image Synthesiscited by 890
  21. 2023Graph of Thoughts: Solving Elaborate Problems with Large Language Modelscited by 886
  22. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 879
  23. 2023Diffusion Model Alignment Using Direct Preference Optimizationcited by 790
  24. 2023Attend-and-Excite: Attention-Based Semantic Guidance for Text-to-Image Diffusion Modelscited by 702
  25. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 516
  26. 2024Generative Verifiers: Reward Modeling as Next-Token Predictioncited by 480
  27. 2023DPOK: Reinforcement Learning for Fine-tuning Text-to-Image Diffusion Modelscited by 450
  28. 2022Training-Free Structured Diffusion Guidance for Compositional Text-to-Image Synthesiscited by 388
  29. 2024ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Searchcited by 344
  30. 2022Selection-Inference: Exploiting Large Language Models for Interpretable Logical Reasoningcited by 334
  31. 2024Hunyuan-DiT: A Powerful Multi-Resolution Diffusion Transformer with Fine-Grained Chinese Understandingcited by 298
  32. 2024Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoningcited by 279
  33. 2021GRAND: Graph Neural Diffusioncited by 258
  34. 2024Stream of Search (SoS): Learning to Search in Languagecited by 145
  35. 2025Can 1B LLM Surpass 405B LLM? Rethinking Compute-Optimal Test-Time Scalingcited by 136
  36. 2024InitNO: Boosting Text-to-Image Diffusion Models via Initial Noise Optimizationcited by 123
  37. 2024Fast Best-of-N Decoding via Speculative Rejectioncited by 112
  38. 2023Noise-Free Score Distillationcited by 99

50 most cited of 69 All 69 (JSON)

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

Similar, not cited

Close in wording, no citation either way

  1. 2025Diffusion Sampling Path Tells More: An Efficient Plug-and-Play Strategy for Sample Filtering
  2. 2026Leveraging Inference-Time Compute for Diffusion Models via Global Scheduling of Denoising Trajectories
  3. 2026Flash-BoN: Instant Drafts for Inference-Time Scaling in Diffusion Models
  4. 2026On the Robustness of Distribution Support under Diffusion Guidance
  5. 2026Guided Trajectory Optimization with Sparse Scaling for Test-Time Diffusion
  6. 2025Training-free Diffusion Acceleration with Bottleneck Sampling
  7. 2026ASSERT: Adaptive Stochastic Sampling for Robust Diffusion Models on Analog Compute-in-Memory Hardware
  8. 2026Couple to Control: Joint Initial Noise Design in Diffusion Models