mlsanityData to 14 Oct 2026

Learning Iterative Reasoning through Energy Diffusion

arXiv 2406.11179 ↗First posted 17 Jun 2024cs.LG cs.AIcited by 36

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Abstract (arXiv)

We introduce iterative reasoning through energy diffusion (IRED), a novel framework for learning to reason for a variety of tasks by formulating reasoning and decision-making problems with energy-based optimization. IRED learns energy functions to represent the constraints between input conditions and desired outputs. After training, IRED adapts the number of optimization steps during inference based on problem difficulty, enabling it to solve problems outside its training distribution -- such as more complex Sudoku puzzles, matrix completion with large value magnitudes, and pathfinding in larger graphs. Key to our method's success is two novel techniques: learning a sequence of annealed energy landscapes for easier inference and a combination of score function and energy landscape supervision for faster and more stable training. Our experiments show that IRED outperforms existing methods in continuous-space reasoning, discrete-space reasoning, and planning tasks, particularly in more challenging scenarios. Code and visualizations at https://energy-based-model.github.io/ired/

Key facts. Cited by 36 papers in the map (data through 14 Oct 2026). Builds on 44 of its 55 references that are in the map. First posted on arXiv 17 Jun 2024.

Builds on

44 of 55 references.

References · 44

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
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32 more
  1. 2020Integrated Task and Motion Planningcited by 290
  2. 2018Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimizationcited by 227
  3. 2023DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimizationcited by 221
  4. 2023Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMCcited by 220
  5. 2016A Theory of Generative ConvNetcited by 174
  6. 2019SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solvercited by 173
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  12. 2020Improved Contrastive Divergence Training of Energy Based Modelscited by 130
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 3; 2025: 14; 2026: 19.

36 papers.

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  1. 2025Hierarchical Reasoning Modelcited by 177
  2. 2025Inference-time Scaling of Diffusion Models through Classical Searchcited by 49
  3. 2024Artificial Kuramoto Oscillatory Neuronscited by 38
  4. 2025Coevolutionary Continuous Discrete Diffusion: Make Your Diffusion Language Model a Latent Reasonercited by 32
  5. 2025Energy-Based Transformers are Scalable Learners and Thinkerscited by 31
  6. 2026Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformerscited by 28
  7. 2024Non-myopic Generation of Language Models for Reasoning and Planningcited by 26
  8. 2025A Formal Comparison Between Chain of Thought and Latent Thoughtcited by 15
  9. 2026Thinking with Looped Flowscited by 9
  10. 2025VFScale: Intrinsic Reasoning through Verifier-Free Test-time Scalable Diffusion Modelcited by 6
  11. 2025Self-Supervised Transformers as Iterative Solution Improvers for Constraint Satisfactioncited by 6
  12. 2025Bottlenecked Transformers: Periodic KV Cache Consolidation for Generalised Reasoningcited by 3
24 more
  1. 2026On the Role of Computation in Reinforcement Learningcited by 3
  2. 2026A Kinetic Energy Perspective of Flow Matchingcited by 3
  3. 2025Hyper-SET: Designing Transformers via Hyperspherical Energy Minimizationcited by 2
  4. 2025Selection, Reflection and Self-Refinement: Revisit Reasoning Tasks via a Causal Lenscited by 2
  5. 2025Generalizable Reasoning through Compositional Energy Minimizationcited by 2
  6. 2025EBT-Policy: Energy Unlocks Emergent Physical Reasoning Capabilitiescited by 2
  7. 2024GenPlan: Generative Sequence Models as Adaptive Plannerscited by 1
  8. 2026Thinking into the Future: Latent Lookahead Training for Transformerscited by 1
  9. 2026Large Neighborhood Search meets Iterative Neural Constraint Heuristicscited by 1
  10. 2026Learning 3D Reconstruction with Priors in Test Timecited by 1
  11. 2025Constraints-Guided Diffusion Reasoner for Neuro-Symbolic Learningcited by 0
  12. 2025PID-controlled Langevin Dynamics for Faster Sampling of Generative Modelscited by 0
  13. 2026Can Continuous-Time Diffusion Models Generate and Solve Globally Constrained Discrete Problems? A Study on Sudokucited by 0
  14. 2026Tutorial on Reasoning for IR & IR for Reasoningcited by 0
  15. 2026Blocked Gibbs meets Diffusion Transformers: Unsupervised Learning for Constraint Optimizationcited by 0
  16. 2026Text Dictates, Music Decorates: Energy-based Attention for Editable Dance Motion Generationcited by 0
  17. 2026Retrieval-Warmed Energy-Based Reasoning: A Five-Arm Ablation Methodology for Diffusion-as-Inference on Structured Reasoning Taskscited by 0
  18. 2026Advancing Optimal Subset Oracle via Learning Relaxation of Neural Set Functionscited by 0
  19. 2026Solver-Hard Is Not Model-Hard: A Hardness-Controlled Diagnostic for LLM Constraint Reasoningcited by 0
  20. 2026Position: Certified Correctness in Neural Constraint Reasoning Requires Symbolic Integrationcited by 0
  21. 2026Composing Flow-Matching Energies with Known Physics: Generation, OOD Detection, and Inversion on PDE Fieldscited by 0
  22. 2026Latent Recurrent Thoughts: Recurrent Refinement of Proposed Latents for Reasoning with Frozen LLMscited by 0
  23. 2026Let It Go or Learn to Self-Correct: Continuous Diffusion for Constrained Discrete Taskscited by 0
  24. 2026Representation-based Masked Diffusion Modelcited by 0