Inference-time selection methods, such as Best-of-N, improve generation by sampling a pool of candidates and selecting the top-ranked completion according to a reward model. Distillation seeks to amortize this procedure into a single policy by replacing raw rewards with in-pool ranks and learning a policy that upweights higher-ranked completions. However, existing rank-based policies typically use smooth full-support reweighting, so low-ranked completions receive less mass but remain in the target support. Although a sharper reweighting reduces lower-tail mass, it also increases reliance on brittle ranking at the top made by a single reward model. We propose TUP: a Truncate-bad, Upweight-good Policy that removes low-ranked completions from the support and reweights only the retained upper tail with a tunable sharpness. TUP admits a closed-form, prompt-independent normalization and can be trained fully offline via binary cross-entropy, using shifted-truncated win-rates as soft labels and distilled-to-reference log-likelihood ratios as logits. Theoretically, under certain assumptions, we show that for any unknown oracle reward, the best monotone rank-reweighting can be matched by a lower-tail truncation rule, providing formal support for removing the lower tail rather than merely downweighting it. Empirically, we show that TUP is competitive with strong offline alignment baselines.
Inference-time scaling for text-to-image generation has progressed from simple Best-of-$N$ (BoN) sampling to guided search methods that verify and steer candidate trajectories at intermediate denoising steps. These approaches focus on when and how often to verify during denoising but largely treat the cost of generation itself as fixed. Moreover, the standard practice of comparing methods by number of function evaluations (NFEs) counts only denoising forward passes and ignores verifier overhead, which can distort efficiency rankings. We show that under wall-clock evaluation, simple BoN already matches or outperforms several guided search techniques, suggesting that compute is better spent on broader exploration than on repeated intermediate verification. This motivates Flash-BoN, which generates a large pool of inexpensive draft candidates by combining three complementary acceleration knobs: timestep truncation, layer skipping, and activation proxies into a single configuration optimized once per model. An efficient multi-stage verification procedure then identifies the most promising draft, which is refined at full quality. Across three benchmarks and three model scales, Flash-BoN consistently outperforms all baselines under fixed wall-clock budgets, with gains that grow at larger model scales (+8% AUC). We further show that our strategy combines well and improves existing orthogonal techniques such as reflection-based prompt optimization (+16% AUC). The gains correlate with increased candidate diversity, which also enables draft-guided selection to accelerate RL post-training convergence.
Inference-time alignment methods, such as Best-of-$N$, offer a flexible alternative to training-based alignment by using reward models to select high-quality responses generated by a reference LLM. However, the efficacy of these methods is inherently limited by the response quality: if the reference LLM assigns negligible probability to high-reward responses, no selection strategy will succeed in finding aligned outputs. In this work, we propose Best-of-Better-$N$ (BoBN), an in context learning-based generation framework to address this challenge. Our method utilizes retrieval from high-reward examples relevant to the input query and task. Crucially, we introduce a restyling step where retrieved responses are rewritten by the reference LLM to align with the target task's format and style. These restyled examples are used in-context to shift the sampling distribution toward the high-reward region. We analytically characterize how in-context learning shifts the output distribution of pretrained transformers toward the high-reward region, resulting in provable benefits on the target task. We then evaluate BoBN on safety alignment and mathematical reasoning benchmarks across several reference LLMs. BoBN's higher-quality responses enable better performance to be achieved when the number of responses $N$ is fixed, and smaller $N$ required to achieve a target performance.