diff --git a/csrc/quantization/compressed_tensors/int8_quant_kernels.cu b/csrc/quantization/compressed_tensors/int8_quant_kernels.cu
index aec9fa002f96e..e9987535bd3ea 100644
--- a/csrc/quantization/compressed_tensors/int8_quant_kernels.cu
+++ b/csrc/quantization/compressed_tensors/int8_quant_kernels.cu
@@ -96,12 +96,15 @@ __global__ void static_scaled_int8_quant_kernel(
     scalar_t const* __restrict__ input, int8_t* __restrict__ out,
     scale_type const* scale_ptr, const int hidden_size) {
   int const tid = threadIdx.x;
-  int const token_idx = blockIdx.x;
+  int64_t const token_idx = blockIdx.x;
   scale_type const scale = *scale_ptr;
 
+  // Must be performed using 64-bit math to avoid integer overflow.
+  out += token_idx * hidden_size;
+  input += token_idx * hidden_size;
+
   for (int i = tid; i < hidden_size; i += blockDim.x) {
-    out[token_idx * hidden_size + i] = float_to_int8_rn(
-        static_cast<float>(input[token_idx * hidden_size + i]) / scale);
+    out[i] = float_to_int8_rn(static_cast<float>(input[i]) / scale);
   }
 }
 
@@ -111,14 +114,18 @@ __global__ void static_scaled_int8_azp_quant_kernel(
     scale_type const* scale_ptr, azp_type const* azp_ptr,
     const int hidden_size) {
   int const tid = threadIdx.x;
-  int const token_idx = blockIdx.x;
+  int64_t const token_idx = blockIdx.x;
   scale_type const scale = *scale_ptr;
   azp_type const azp = *azp_ptr;
 
+  // Must be performed using 64-bit math to avoid integer overflow.
+  out += token_idx * hidden_size;
+  input += token_idx * hidden_size;
+
   for (int i = tid; i < hidden_size; i += blockDim.x) {
-    auto const val = static_cast<float>(input[token_idx * hidden_size + i]);
+    auto const val = static_cast<float>(input[i]);
     auto const quant_val = int32_to_int8(float_to_int32_rn(val / scale) + azp);
-    out[token_idx * hidden_size + i] = quant_val;
+    out[i] = quant_val;
   }
 }
 
@@ -127,12 +134,16 @@ __global__ void dynamic_scaled_int8_quant_kernel(
     scalar_t const* __restrict__ input, int8_t* __restrict__ out,
     scale_type* scale, const int hidden_size) {
   int const tid = threadIdx.x;
-  int const token_idx = blockIdx.x;
+  int64_t const token_idx = blockIdx.x;
   float absmax_val = 0.0f;
   float const zero = 0.0f;
 
+  // Must be performed using 64-bit math to avoid integer overflow.
+  out += token_idx * hidden_size;
+  input += token_idx * hidden_size;
+
   for (int i = tid; i < hidden_size; i += blockDim.x) {
-    float val = static_cast<float>(input[token_idx * hidden_size + i]);
+    float val = static_cast<float>(input[i]);
     val = val > zero ? val : -val;
     absmax_val = val > absmax_val ? val : absmax_val;
   }
@@ -150,8 +161,7 @@ __global__ void dynamic_scaled_int8_quant_kernel(
 
   float const tmp_scale = 127.0f / block_absmax_val;
   for (int i = tid; i < hidden_size; i += blockDim.x) {
-    out[token_idx * hidden_size + i] = float_to_int8_rn(
-        static_cast<float>(input[token_idx * hidden_size + i]) * tmp_scale);
+    out[i] = float_to_int8_rn(static_cast<float>(input[i]) * tmp_scale);
   }
 }
 
@@ -159,13 +169,17 @@ template <typename scalar_t, typename scale_type, typename azp_type>
 __global__ void dynamic_scaled_int8_azp_quant_kernel(
     scalar_t const* __restrict__ input, int8_t* __restrict__ out,
     scale_type* scale, azp_type* azp, const int hidden_size) {
-  int const token_idx = blockIdx.x;
+  int64_t const token_idx = blockIdx.x;
+
+  // Must be performed using 64-bit math to avoid integer overflow.
+  out += token_idx * hidden_size;
+  input += token_idx * hidden_size;
 
   // Scan for the min and max value for this token
   float max_val = std::numeric_limits<float>::min();
   float min_val = std::numeric_limits<float>::max();
   for (int i = threadIdx.x; i < hidden_size; i += blockDim.x) {
-    auto val = static_cast<float>(input[token_idx * hidden_size + i]);
+    auto val = static_cast<float>(input[i]);
     max_val = std::max(max_val, val);
     min_val = std::min(min_val, val);
   }
@@ -200,10 +214,10 @@ __global__ void dynamic_scaled_int8_azp_quant_kernel(
 
   // Quantize the values
   for (int i = threadIdx.x; i < hidden_size; i += blockDim.x) {
-    auto const val = static_cast<float>(input[token_idx * hidden_size + i]);
+    auto const val = static_cast<float>(input[i]);
     auto const quant_val =
         int32_to_int8(float_to_int32_rn(val / scale_val) + azp_val);
-    out[token_idx * hidden_size + i] = quant_val;
+    out[i] = quant_val;
   }
 }
 
diff --git a/vllm/_custom_ops.py b/vllm/_custom_ops.py
index c6e5bed5ad9a3..f09e33c5f5815 100644
--- a/vllm/_custom_ops.py
+++ b/vllm/_custom_ops.py
@@ -517,7 +517,6 @@ def selective_scan_fwd_fake(u: torch.Tensor, delta: torch.Tensor,
 def cutlass_scaled_mm_supports_fp8(cuda_device_capability: int) -> bool:
     return torch.ops._C.cutlass_scaled_mm_supports_fp8(cuda_device_capability)
 
-
 def cutlass_scaled_mm(a: torch.Tensor,
                       b: torch.Tensor,
                       scale_a: torch.Tensor,
@@ -531,9 +530,15 @@ def cutlass_scaled_mm(a: torch.Tensor,
 
     m = a.shape[0]
     n = b.shape[1]
-    out = torch.empty((m, n), dtype=out_dtype, device=a.device)
 
-    torch.ops._C.cutlass_scaled_mm(out, a, b, scale_a, scale_b, bias)
+    if is_hip():
+        out = torch.mm(a.to(torch.float32), b.to(torch.float32))
+        out = scale_a * out
+        out = scale_b.T * out
+        out = out.to(out_dtype)
+    else:
+        out = torch.empty((m, n), dtype=out_dtype, device=a.device)
+        torch.ops._C.cutlass_scaled_mm(out, a, b, scale_a, scale_b, bias)
 
     return out