Learning From Corrupt Data

Sept 11, 2025

Adam Wei

Agenda

  1. Book-keeping Items
  2. Improved performance
  3. Scaling Issues
  4. "Locality Experiment"

Book-Keeping Items

  • Co-training paper was accepted to "Making Sense of Data in Robotics," CoRL
  • Other projects
    • Pushing for ICRA...
    • Privacy project!

Part 1

Sweeps and Performance Improvements

Project Outline

North Star Goal: Train with internet scale data (Open-X, AgiBot, etc)

Stepping Stone Experiments:

  • Motion planning
  • Sim-and-real co-training (planar pushing)
  • Cross-embodied data (Lu's data)
  • Bin picking

Last Time: How to choose \(\sigma_{min}\)

\(\sigma_{min}^i = \inf\{\sigma\in[0,1]: c_\theta (x_\sigma, \sigma) > 0.5-\epsilon\}\)

\(\implies \sigma_{min}^i = \inf\{\sigma\in[0,1]: d_\mathrm{TV}(p_\sigma, q_\sigma) < \epsilon\}\)*

* assuming \(c_\theta\) is perfectly trained

Last time: Which Classifier To Use?

Performance is sensitive to classifier and \(\sigma_{min}\) choice!

Sim & Real Cotraining

Performance vs Classifier Epoch

Sim & Real Cotraining

Choosing \(\tau = 0.5-\epsilon\)

\(\sigma_{min}^i = \inf\{\sigma\in[0,1]: c_\theta (x_\sigma, \sigma) > 0.5-\epsilon\}\)

\(\implies \sigma_{min}^i = \inf\{\sigma\in[0,1]: d_\mathrm{TV}(p_\sigma, q_\sigma) < \epsilon\}\)*

Sim & Real Cotraining

Performance vs Classifier Threshold

Sim & Real Cotraining

Performance vs Classifier Threshold

Sim & Real Cotraining

Performance vs Sim Demos: 10 Real Demos

Sim & Real Cotraining

Performance vs Sim Demos: 50 Real Demos

Part 2

Scaling and Algorithmic Issues

Denoising Loss vs Ambient Loss

Ambient Diffusion: Scaling \(|\mathcal{D}_S|\)

Hypothesis: As sim data increases, ambient diffusion approaches "sim-only" training, which harms performance.

\(|\mathcal{D}_S|=500\)

\(|\mathcal{D}_S|=4000\)

Denoising Loss vs Ambient Loss

Ambient Diffusion: Scaling \(|\mathcal{D}_S|\)

Thought experiment

\(\mathcal{X} = \{-1, 0, 1\}\)

Choosing \(\sigma_{min}\) per dataset

Classifier assigns some \(\sigma_{min}\) to all datapoints from \(q_0\)

\(p_0\) samples 0 and 1 w.p. 0.5

\(q_0\) samples -1 and 0 w.p. 0.5

Choosing \(\sigma_{min}\) per datapoint

Classifier assigns \(\sigma_{min}=0\) to all 0's in \(q_0\) and \(\sigma_{min}=1\) to all -1's

\(\implies\) model sees more 0's during training \(\implies\) heavily biased model!

Denoising Loss vs Ambient Loss

Possible Solutions

Choosing \(\sigma_{min}\) per "bucket"

  • Split dataset into N buckets (ex. randomly)
  • Assign \(\sigma_{min}\) per bucket
    • "Can't do statistics with n=1" - Costis

"Soft" Ambient Diffusion

  • Instead of having a hard \(\sigma_{min}\) cutoff, use a softer version
  • Need to figure out what this soft "mixing" function looks like
    • Some theoretical ideas here... WIP

Part 3

Locality and \(\sigma_{max}\)

Denoising Loss vs Ambient Loss

Locality Experiments

Ambient Diffusion: "use low-quality data at high noise levels"

Ambient Diffusion Omni: "use OOD with local similarity at low noise levels"

Intuition

  1. Real-world data exhibits "locality"
  2. At low-noise levels, diffusion uses a "small receptive field"

 

Therefore, we can use OOD data to learn local features at low noise levels

Denoising Loss vs Ambient Loss

Locality

Which photo is the cat?

Denoising Loss vs Ambient Loss

Locality

Which photos is the cat?

Denoising Loss vs Ambient Loss

Locality

Which photo is the cat?

Denoising Loss vs Ambient Loss

Locality

Denoising Loss vs Ambient Loss

Locality

Denoising Loss vs Ambient Loss

Receptive Field

Denoising Loss vs Ambient Loss

Receptive Field

Denoising Loss vs Ambient Loss

Locality Experiments

Ambient Diffusion Omni: "use OOD with local similarity at low noise levels"

Intuition: If the receptive field at \(\sigma_{max}\) is sufficiently small that you cannot distinguish cats from dogs, then you can use cats to train a generator for dogs

Denoising Loss vs Ambient Loss

Ambient Diffusion Omni

Repeat:

  1. Sample (O, A, \(\sigma_{min}\), \(\sigma_{max}\)) ~ \(\mathcal{D}\)
  2. Choose noise level \(\sigma \in \{\sigma \in [0,1] : \sigma \geq \sigma_{min} \mathrm{\ or\ } \sigma \leq \sigma_{max}\}\)
  3. Optimize loss

\(\sigma=0\)

\(\sigma_{max}\)

Corrupt Data (\(\sigma\geq\sigma_{min}\))

Clean Data

Corrupt Data (\(\sigma\leq\sigma_{max}\))

\(\sigma_{min}\)

Denoising Loss vs Ambient Loss

Connection to Robotics

Locality in robotics:

  • Smoothness
  • Constraint satisfaction
  • "Motion-level correctness"

Experiment:

(equivalent to cats vs dogs experiment in ambient diffusion omni)

  • Clean data: sorts objects into bins
  • Corrupt dataset 1: places objects into any bin
  • Corrupt dataset 2: Open-X pick-and-place data