The Gaussian Is Enough: Flow-Matching Priors Do Not Help When Fine-Tuning Large Behavior Models

Technical Summary: The Gaussian Is Enough for Fine-Tuning Large Behavior Models

Problem Statement
Modern robot imitation learning increasingly utilizes generative policies based on diffusion or flow-matching models. These models generate actions by transporting samples from a prior distribution $p_0$ to a target action distribution conditioned on observations. While recent work has demonstrated that replacing the standard isotropic Gaussian prior with a non-Gaussian, "closer-to-target" prior substantially improves performance when training policies from scratch, it remains unknown whether these benefits transfer to the fine-tuning of pretrained Large Behavior Models (LBMs). LBMs, such as LBM 1.0, $\pi_0.5$, and GR00T N1.5, are typically pre-trained on diverse data and then fine-tuned on specific tasks. The central question addressed is: Does initializing the fine-tuning process with an informed, non-Gaussian action prior (e.g., actions sampled from the pretrained model itself) yield better performance than the standard Gaussian prior?

Methodology
The authors conducted a large-scale empirical study involving over 100,000 simulation rollouts across 40+ tasks in two simulation platforms (LBM Eval and RoboCasa365) and 1,250 hardware rollouts on five bimanual manipulation tasks.

1. Prior Variants: The study compared seven distinct prior constructions:

   • Standard Baseline: Isotropic Gaussian $Z \sim \mathcal{N}(0, I)$.
   • Proposed Priors (derived from the pretrained LBM $\pi_{pre}$):
     • $A_{pre}$: Actions generated by a frozen copy of the pretrained policy (partially denoised).
     • $A_{pre} + \sigma_A Z$: $A_{pre}$ with added Gaussian noise in action space.
     • $E_{pre} + \sigma_E Z$: Pretrained encoder embeddings with added Gaussian noise, used to generate actions.
   • Literature Baselines: Cocos (condition-dependent Gaussian), BRIDGER (CVAE-based prior), and Retrieval (k-NN based prior).

2. Experimental Settings:

   • Setting A: Controlled comparison using an artificially strong prior (a checkpoint fine-tuned on 50% of data) to ensure the prior was measurably closer to the target in $\ell_2$ distance.
   • Setting B (Sim & Real): Fine-tuning LBM 1.0 across varying data fractions (5% to 100%) in simulation and on physical hardware (Franka FR3 arms).
   • Setting C: Validation across different LBM architectures ($\pi_0.5$ and GR00T N1.5) on the RoboCasa benchmark.

3. Analysis & Diagnostics:

   • Performance Metrics: Success rates and partial task progress, evaluated using rigorous statistical testing (STEP framework for binary outcomes, Welch's t-test for continuous metrics, with Bonferroni correction).
   • Introspective Metrics: LogME (training-free feature quality), per-observation $\ell_2$ distance, and cosine similarity in both action space and embedding space.
   • Ablation: A learning-rate ablation was performed to isolate the impact of encoder training versus prior choice.

Key Results
The study consistently finds that non-Gaussian priors, even those demonstrably closer to the target distribution, do not improve fine-tuning performance compared to the standard Gaussian prior.

• Performance Equivalence: Across all architectures, data fractions (except one specific low-data case), and environments (simulation and hardware), the success rates of policies fine-tuned with non-Gaussian priors were statistically indistinguishable from, or occasionally worse than, those fine-tuned with a Gaussian prior.
• The "Closer" Prior Paradox: In Setting A, the non-Gaussian prior $A_{pre}$ was $3\times$ closer to the target actions than the Gaussian prior. While this yielded significant gains when training from scratch, it provided no advantage during fine-tuning.
• Low-Data Exception: A marginal benefit was observed only in the very low-data regime (5% of demonstrations, approx. 10–20 examples) where the embedding-space jitter prior ($E_{pre} + \sigma_E Z$) outperformed the Gaussian.
• Architectural Generalization: The negative result held true for LBM 1.0, $\pi_0.5$, and GR00T N1.5.

Diagnostic Findings: Why Priors Do Not Matter
The authors provide a mechanistic explanation for this phenomenon through three diagnostics:

1. Feature Quality: Fine-tuned encoders produce features of equal predictive power (measured by LogME) regardless of the prior used.
2. Action Convergence: Post-fine-tuning action predictions converge to similar distances from the ground truth across all priors.
3. Representation Divergence: Despite similar outputs, the internal representations diverge significantly. The Gaussian prior causes the encoder to change the least from its pretrained state, while non-Gaussian priors (especially $A_{pre}$) force the encoder to restructure substantially to compensate for the shifted prior.
4. Dominant Factor: A learning-rate ablation confirmed that the quality of the observation encoder is the dominant factor in performance. Reducing the encoder's learning rate caused a massive drop in success rates (15–17%), whereas changing the prior within a fixed learning rate regime had negligible effects.

Significance and Claims
The paper concludes that for the fine-tuning of Large Behavior Models, the standard Gaussian prior is a sufficient and well-supported choice. The study challenges the intuition that a "closer" prior facilitates fine-tuning by reducing transport distance in action space. Instead, the results suggest that:

• The pretrained encoder is the primary driver of fine-tuning success.
• The prior choice influences the optimization trajectory and the degree of encoder restructuring but does not affect the final policy performance.
• Implementing complex, learned priors adds engineering overhead without measurable benefits in the fine-tuning regime.

The authors position this work as the first large-scale study of non-Gaussian priors for LBM fine-tuning, offering a negative result that redirects future research toward understanding the learning dynamics of the encoder and the conditions under which priors might still matter (e.g., the very low-data regime).