diff --git a/src/ATen/native/xpu/sycl/HermitePolynomialHKernel.cpp b/src/ATen/native/xpu/sycl/HermitePolynomialHKernel.cpp
index 4862af9a8f..bffd6117b5 100644
--- a/src/ATen/native/xpu/sycl/HermitePolynomialHKernel.cpp
+++ b/src/ATen/native/xpu/sycl/HermitePolynomialHKernel.cpp
@@ -9,17 +9,15 @@ namespace at::native::xpu {
 template <typename scalar_t>
 struct HermitePolynomialHFunctor {
   scalar_t operator()(scalar_t x, scalar_t n_) const {
-    int64_t n = static_cast<int64_t>(n_);
+    auto n = static_cast<int64_t>(n_);
     if (n < 0) {
       return scalar_t(0.0);
-    }
-
-    if (n == 0) {
+    } else if (n == 0) {
       return scalar_t(1.0);
-    }
-
-    if (n == 1) {
+    } else if (n == 1) {
       return x + x;
+    } else if (n > getHermitianLimit<scalar_t>()) {
+      return std::numeric_limits<scalar_t>::quiet_NaN();
     }
 
     scalar_t p = scalar_t(1.0);
diff --git a/src/ATen/native/xpu/sycl/HermitePolynomialHeKernel.cpp b/src/ATen/native/xpu/sycl/HermitePolynomialHeKernel.cpp
index 6c37e87202..8ba1d8bfff 100644
--- a/src/ATen/native/xpu/sycl/HermitePolynomialHeKernel.cpp
+++ b/src/ATen/native/xpu/sycl/HermitePolynomialHeKernel.cpp
@@ -9,17 +9,15 @@ namespace at::native::xpu {
 template <typename scalar_t>
 struct HermitePolynomialHeFunctor {
   scalar_t operator()(scalar_t x, scalar_t n_) const {
-    int64_t n = static_cast<int64_t>(n_);
+    auto n = static_cast<int64_t>(n_);
     if (n < 0) {
       return scalar_t(0.0);
-    }
-
-    if (n == 0) {
+    } else if (n == 0) {
       return scalar_t(1.0);
-    }
-
-    if (n == 1) {
+    } else if (n == 1) {
       return x;
+    } else if (n > getHermitianLimit<scalar_t>()) {
+      return std::numeric_limits<scalar_t>::quiet_NaN();
     }
 
     scalar_t p = scalar_t(1.0);
diff --git a/src/ATen/native/xpu/sycl/LaguerrePolynomialLKernel.cpp b/src/ATen/native/xpu/sycl/LaguerrePolynomialLKernel.cpp
index 8688f80456..869d64492a 100644
--- a/src/ATen/native/xpu/sycl/LaguerrePolynomialLKernel.cpp
+++ b/src/ATen/native/xpu/sycl/LaguerrePolynomialLKernel.cpp
@@ -30,7 +30,7 @@ struct LaguerrePolynomialLFunctor {
     scalar_t q = scalar_t(1.0) - x;
     scalar_t r;
 
-    for (int64_t k = 1; k < n; k++) {
+    for (int64_t k = 1; (k < n) && !std::isnan(q); k++) {
       r = (((k + k) + (scalar_t(1.0) - x)) * q - k * p) / (k + 1);
       p = q;
       q = r;
diff --git a/src/ATen/native/xpu/sycl/LegendrePolynomialPKernel.cpp b/src/ATen/native/xpu/sycl/LegendrePolynomialPKernel.cpp
index 2176c4e79c..caf1d8ac16 100644
--- a/src/ATen/native/xpu/sycl/LegendrePolynomialPKernel.cpp
+++ b/src/ATen/native/xpu/sycl/LegendrePolynomialPKernel.cpp
@@ -34,7 +34,7 @@ struct LegendrePolynomialPFunctor {
     scalar_t q = x;
     scalar_t r;
 
-    for (int64_t k = 1; k < n; k++) {
+    for (int64_t k = 1; (k < n) && !std::isnan(q); k++) {
       r = ((k + k + 1) * x * q - k * p) / (k + 1);
       p = q;
       q = r;
diff --git a/test/xpu/skip_list_common.py b/test/xpu/skip_list_common.py
index 5e70eebf44..9eeb6b44c4 100644
--- a/test/xpu/skip_list_common.py
+++ b/test/xpu/skip_list_common.py
@@ -74,12 +74,6 @@
         "test_compare_cpu_linalg_lu_factor_ex_xpu_float32",
         "test_compare_cpu_linalg_lu_factor_xpu_float32",
         "test_compare_cpu_linalg_lu_xpu_float32",
-        # XPU hang. CUDA hang as well.
-        # https://github.com/pytorch/pytorch/issues/79528
-        "test_compare_cpu_special_hermite_polynomial_he_xpu_float32",
-        "test_compare_cpu_special_hermite_polynomial_h_xpu_float32",
-        "test_compare_cpu_special_laguerre_polynomial_l_xpu_float32",
-        "test_compare_cpu_special_legendre_polynomial_p_xpu_float32",
         # core dump
         "test_dtypes__refs_nn_functional_pdist_xpu",
         # XFAIL of CUDA and XPU, unexpected success in fallback