# SCAMP: Sparse-anchor Control is One Small Projection

arXiv: https://arxiv.org/abs/2605.14716 · HTML: https://mlsanity.com/paper/2605.14716/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 41 references that are in the map.
- First posted on arXiv 14 May 2026.

## Builds on (most cited first, 27 of 27)

- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Human Motion Diffusion Model](https://mlsanity.com/paper/2209.14916/) (2022)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (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)
- [MoMask: Generative Masked Modeling of 3D Human Motions](https://mlsanity.com/paper/2312.00063/) (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)
- [FreeDoM: Training-Free Energy-Guided Conditional Diffusion Model](https://mlsanity.com/paper/2303.09833/) (2023)
- [OmniControl: Control Any Joint at Any Time for Human Motion Generation](https://mlsanity.com/paper/2310.08580/) (2023)
- [Guided Motion Diffusion for Controllable Human Motion Synthesis](https://mlsanity.com/paper/2305.12577/) (2023)
- [MotionLCM: Real-time Controllable Motion Generation via Latent Consistency Model](https://mlsanity.com/paper/2404.19759/) (2024)
- [Optimizing Diffusion Noise Can Serve As Universal Motion Priors](https://mlsanity.com/paper/2312.11994/) (2023)
- [TLControl: Trajectory and Language Control for Human Motion Synthesis](https://mlsanity.com/paper/2311.17135/) (2023)
- [Rethinking Diffusion for Text-Driven Human Motion Generation: Redundant Representations, Evaluation, and Masked Autoregression](https://mlsanity.com/paper/2411.16575/) (2024)
- [Flexible Motion In-betweening with Diffusion Models](https://mlsanity.com/paper/2405.11126/) (2024)
- [Theseus: A Library for Differentiable Nonlinear Optimization](https://mlsanity.com/paper/2207.09442/) (2022)
- [Motion Anything: Any to Motion Generation](https://mlsanity.com/paper/2503.06955/) (2025)
- [MaskControl: Spatio-Temporal Control for Masked Motion Synthesis](https://mlsanity.com/paper/2410.10780/) (2024)
- [Kimodo: Scaling Controllable Human Motion Generation](https://mlsanity.com/paper/2603.15546/) (2026)

## Abstract (arXiv)

Authoring with a text-to-motion generator needs sparse anchors: chosen joints, at chosen frames, at given positions. Meeting them currently costs a conditioning branch trained for the task, or hundreds of per-clip optimisation steps in the architecture's native variables. In any generator that decodes a continuous state through a frozen differentiable decoder, the anchors ask for little and leave most of the state free: a few hundred numbers against a state of tens of thousands. Every control method is a choice among the states that satisfy them, and the choices differ along the directions the anchors cannot see and the motion can. SCAMP makes the choice that moves none of them: damped Gauss-Newton in the space of the anchors, through the frozen decoder alone, training-free, with one dimensionless damping constant. Every increment is a combination of the rows of the anchors' Jacobian, so the correction is orthogonal to everything the anchors never see, and the system solved is the size of the request rather than of the state. Applied unchanged to seven published generators spanning diffusion, token and latent designs, it matches or exceeds in anchor error every released control method it is measured against, and closes the anchors on hosts that ship none. Confined to those rows, a correction can only take the shapes the decoder admits, so what it costs belongs to the decoder, and holding the solver fixed makes that cost measurable: it divides by decoder family, windowed decoders staying within a small multiple of the unconstrained generator's foot skating where analytic recoveries multiply it several times over. Built to that criterion, our own generator reaches 0.083 m anchor error at FID 0.102 in 0.50 s per clip. The decoder's temporal support is a design criterion for controllable motion generation.