diff --git a/botorch/posteriors/fully_bayesian.py b/botorch/posteriors/fully_bayesian.py
index 3084a743d2..9b36553f36 100644
--- a/botorch/posteriors/fully_bayesian.py
+++ b/botorch/posteriors/fully_bayesian.py
@@ -3,8 +3,8 @@
 # This source code is licensed under the MIT license found in the
 # LICENSE file in the root directory of this source tree.
 
+from __future__ import annotations
 
-from functools import lru_cache
 from typing import Callable, Optional, Tuple
 
 import torch
@@ -54,6 +54,30 @@ def batched_bisect(
     return center
 
 
+def _quantile(posterior: FullyBayesianPosterior, value: Tensor) -> Tensor:
+    r"""Compute the posterior quantiles for the mixture of models."""
+    if value.numel() > 1:
+        return torch.stack(
+            [_quantile(posterior=posterior, value=v) for v in value], dim=0
+        )
+    if value <= 0 or value >= 1:
+        raise ValueError("value is expected to be in the range (0, 1).")
+    dist = torch.distributions.Normal(
+        loc=posterior.mean, scale=posterior.variance.sqrt()
+    )
+    if posterior.mean.shape[MCMC_DIM] == 1:  # Analytical solution
+        return dist.icdf(value).squeeze(MCMC_DIM)
+    icdf_val = dist.icdf(value)
+    low = icdf_val.min(dim=MCMC_DIM).values - TOL
+    high = icdf_val.max(dim=MCMC_DIM).values + TOL
+    bounds = torch.cat((low.unsqueeze(0), high.unsqueeze(0)), dim=0)
+    return batched_bisect(
+        f=lambda x: dist.cdf(x.unsqueeze(MCMC_DIM)).mean(dim=MCMC_DIM),
+        target=value.item(),
+        bounds=bounds,
+    )
+
+
 class FullyBayesianPosterior(GPyTorchPosterior):
     r"""A posterior for a fully Bayesian model.
 
@@ -82,30 +106,6 @@ def __init__(self, distribution: MultivariateNormal) -> None:
         self._mixture_mean: Optional[Tensor] = None
         self._mixture_variance: Optional[Tensor] = None
 
-        # using lru_cache on methods can cause memory leaks. See flake8 B019
-        # So we define a function here instead, to be called by self.quantile
-        @lru_cache
-        def _quantile(value: Tensor) -> Tensor:
-            r"""Compute the posterior quantiles for the mixture of models."""
-            if value.numel() > 1:
-                return torch.stack([self.quantile(v) for v in value], dim=0)
-            if value <= 0 or value >= 1:
-                raise ValueError("value is expected to be in the range (0, 1).")
-            dist = torch.distributions.Normal(loc=self.mean, scale=self.variance.sqrt())
-            if self.mean.shape[MCMC_DIM] == 1:  # Analytical solution
-                return dist.icdf(value).squeeze(MCMC_DIM)
-            icdf_val = dist.icdf(value)
-            low = icdf_val.min(dim=MCMC_DIM).values - TOL
-            high = icdf_val.max(dim=MCMC_DIM).values + TOL
-            bounds = torch.cat((low.unsqueeze(0), high.unsqueeze(0)), dim=0)
-            return batched_bisect(
-                f=lambda x: dist.cdf(x.unsqueeze(MCMC_DIM)).mean(dim=MCMC_DIM),
-                target=value.item(),
-                bounds=bounds,
-            )
-
-        self._quantile = _quantile
-
     @property
     def mixture_mean(self) -> Tensor:
         r"""The posterior mean for the mixture of models."""
@@ -126,7 +126,7 @@ def mixture_variance(self) -> Tensor:
 
     def quantile(self, value: Tensor) -> Tensor:
         r"""Compute the posterior quantiles for the mixture of models."""
-        return self._quantile(value)
+        return _quantile(posterior=self, value=value)
 
     @property
     def batch_range(self) -> Tuple[int, int]: